UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C.

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 August 2025

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 ☐

Attached as Exhibit I hereto is a copy of the press release of Capital Clean Energy Carriers Corp. announcing the sale of a Neo-Panamax 13,312 TEU container vessel and the securing of financing for six dual fuel medium gas carriers.

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.

	CAPITAL CLEAN ENERGY CARRIERS CORP.
Dated: September 10, 2025	/s/ Gerasimos (Jerry) Kalogiratos
	Name: Gerasimos (Jerry) Kalogiratos
	Title: Chief Executive Officer