UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

Pursuant to Rule 13a-16 or 15d-16

under the Securities Exchange Act of 1934

For the month of January 2026

COMMISSION FILE NUMBER: 001-33373

CAPITAL CLEAN ENERGY CARRIERS CORP.

(Translation of registrant’s name into English)

3 Iassonos Street

Piraeus, 18537 Greece

(Address of principal executive offices)

Indicate by check mark whether the Registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F ☒   Form 40-F ☐

Sale of Neo-Panamax 13,696 TEU container vessel M/V Buenaventura Express

On October 29, 2025, Capital Clean Energy Carriers Corp. (the “Company” or “CCEC”) signed a memorandum of agreement with a third party for the sale of the M/V Buenaventura Express (142,411 DWT / 13,696 TEU, hybrid scrubber-fitted, eco container vessel, built 2023, Hyundai Samho Industries Co. Ltd, South Korea). The vessel was delivered to its new owners on January 19, 2026, and we recognized a total book gain from the sale of $4.2 million. Cash proceeds were used to pay down outstanding debt of $84.4 million and for general corporate purposes. The divestment of this additional container vessel is consistent with the Company’s stated strategy to shift our strategic focus towards the transportation of various forms of gas to industrial customers, including liquefied natural gas (“LNG”) and emerging new commodities in connection with the energy transition. Since February 2024, CCEC has sold 14 container vessels generating gross proceeds of approximately $814.3 million. Following this sale, the Company retains only one 13,312 TEU container vessel in its fleet, which is on long-term time charter through 2033, with options to extend up to 2039.

Order for three latest specification liquefied natural gas carriers to be delivered in 2028 and 2029

On December 29, 2025, the Company announced it has ordered three latest technology LNG carriers (“LNG/Cs”) to be built at HD Hyundai Samho Co., Ltd in South Korea, scheduled for delivery in 2028 and 2029. Specifically, one vessel is scheduled for delivery in the third quarter of 2028 and two further deliveries are scheduled in the first quarter of 2029. The en-bloc ship building price of these vessels is $769.5 million.

With its latest order for three additional LNG/Cs, the Company has 12 LNG/Cs currently in the water and nine LNG/Cs on order (“Newbuild LNG/Cs”). In addition, CCEC has on order an additional nine gas carriers, including three handy liquid CO₂ (“LCO₂”)/multi-gas carriers and six dual-fuel medium gas carriers (the “Gas Fleet”), with deliveries starting in the second quarter of 2026.

Delivery of 22,000 cubic meter low-pressure liquid CO₂ carrier LCO₂ Active

On January 6, 2026, the Company announced the delivery of the world’s first 22,000 cubic meters (“cbm”) low-pressure LCO₂ carrier, the LCO₂ Active, from Hyundai Mipo Dockyard Co., Ltd. (“HMD”). The LCO₂ Active is the first of four 22,000 cbm LCO₂/multi gas carriers under CCEC’s investment program at HMD. The vessel is designed to transport LCO₂, while remaining fully competitive in the conventional handy semi-refrigerated gas carrier market, as these ships feature multi-cargo capability and can carry LCO₂, liquefied petroleum gas (“LPG”), ammonia and selected petrochemicals.

The LCO₂ Active commenced a six-month time charter transporting LPG for an energy trading company, with an option to extend the charter for an additional six months.

The acquisition of the LCO₂ Active was financed with $29.4 million of cash on hand and a 12-year export credit agency-backed loan of $48.9 million. The loan is repayable in 48 quarterly instalments of $0.6 million, with a balloon payment of $18.0 million payable with the final instalment in January 2033. The Company may borrow an additional amount of up to $7.5 million if the vessel secures longer term employment.

As a result of the Company’s contracting for the three additional LNG/Cs and the delivery of the LCO₂ Active, the Company’s capital expenditure schedule (“CAPEX”) has been revised as follows:

Capex Schedule of CCEC in USD million, as of December 31, 2025:

The Company has paid as of December 31, 2025, $704.9 million in advances and deposits towards the acquisition of its under-construction fleet. The final instalment for the delivery of the LCO₂ Active was paid in December 2025.

Quarterly Common Share Cash Dividend

On January 22, 2026, the Company’s board of directors declared a cash dividend of $0.15 per common share for the fourth quarter of 2025, which will be paid on February 12, 2026, to common shareholders of record on February 3, 2026. Attached as Exhibit I hereto is a copy of the press release of CCEC announcing the declaration of the quarterly dividend.

Forward-Looking Statements

The statements in this report on Form 6-K that are not historical facts, including, among other things, statements related to CCEC’s ability to pursue growth opportunities and CCEC’s expectations or objectives regarding future vessel deliveries and charter rate expectations, are forward-looking statements (as such term is defined in Section 21E of the Securities Exchange Act of 1934, as amended). These forward-looking statements involve risks and uncertainties that could cause the stated or forecasted results to be materially different from those anticipated. For a discussion of factors that could materially affect the outcome of forward-looking statements and other risks and uncertainties, see “Risk Factors” in our annual report filed with the SEC on Form 20-F for the year ended December 31, 2024, filed on April 17, 2025. Unless required by law, CCEC expressly disclaims any obligation to update or revise any of these forward-looking statements, whether because of future events, new information, a change in its views or expectations, to conform them to actual results or otherwise. CCEC does not assume any responsibility for the accuracy and completeness of the forward-looking statements. You are cautioned not to place undue reliance on forward-looking statements.

The information contained in this report on Form 6-K is hereby incorporated by reference into the Company’s Registration Statement on Form F-3 (File No. 333-282610), Registration Statement on Form F-3 (File No. 333-286825) and Registration Statement on Form F-3 (File No. 333-287895).

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Exhibit I

Capital Clean Energy Carriers Corp. Declares Quarterly Dividend

January 22, 2026

ATHENS, GREECE, January 22, 2026 (GLOBE NEWSWIRE) – Capital Clean Energy Carriers Corp. (NASDAQ: CCEC) today announced that its board of directors has declared a cash dividend per share of $0.15 for the fourth quarter of 2025 ended December 31, 2025.

The cash dividend for the fourth quarter of 2025 will be paid on February 12, 2026, to common shareholders of record on February 3, 2026.

The Company has implemented a Dividend Reinvestment Plan (“DRIP”) whereby common shareholders can elect to have dividends reinvested directly into additional common shares issued by the Company. To participate in the DRIP for the fourth quarter of 2025, the election deadline is February 2, 2026. For additional information on the plan, including the forms needed to enroll, please visit the website of Computershare Trust Company, N.A., the Company’s transfer agent administering the DRIP, at: www.computershare.com/investor.

The information on www.computershare.com/investor is not incorporated by reference into this press release and should not be considered part of this press release.

This press release does not constitute an offer to sell or the solicitation of an offer to buy any common shares or any other securities, nor will there be any sale of common shares or any other securities in any state or other jurisdiction in which such offer, solicitation or sale would be unlawful prior to registration or qualification under the securities laws of any such state or other jurisdiction.

About Capital Clean Energy Carriers Corp.

Capital Clean Energy Carriers Corp. (NASDAQ: CCEC), an international shipping company, is a leading platform of gas carriage solutions with a focus on the energy transition. CCEC’s in-the-water fleet includes 14 high specification vessels, including 12 latest generation LNG carriers (“LNG/C”), one legacy Neo-Panamax container vessel and one handy LCO₂/multi-gas carrier. In addition, CCEC’s under-construction fleet includes nine additional latest generation LNG/Cs, six dual-fuel medium gas carriers and three handy LCO₂/multi-gas carriers, to be delivered between the second quarter of 2026 and the first quarter of 2029.

For more information about CCEC, please visit: www.capitalpplp.com

Forward-Looking Statements

The statements in this press release that are not historical facts may be forward-looking statements (as such term is defined in Section 21E of the Securities Exchange Act of 1934, as amended). These forward-looking statements involve risks and uncertainties that could cause the stated or forecasted results to be materially different from those anticipated. Unless required by law, we expressly disclaim any obligation to update or revise any of these forward-looking statements, whether because of future events, new information, a change in our views or expectations, to conform them to actual results or otherwise. We assume no responsibility for the accuracy and completeness of the forward-looking statements. We make no prediction or statement about the performance of our common shares.

Contact Details:

Investor Relations / Media

Brian Gallagher

EVP Investor Relations

Tel. +44-(770) 368 4996

E-mail: b.gallagher@capitalmaritime.com

Nicolas Bornozis

Capital Link, Inc. (New York)

Tel. +1-212-661-7566

E-mail: cplp@capitallink.com

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