Eight sailors have also been dismissed from the Stout, The (Norfolk) Virginian-Pilot reported.
The Stout, a guided missile destroyer, is based in Norfolk and is now deployed in the Mediterranean.
Commander Nathan Borchers and Master Chief Susan Bruce-Ross have been reassigned to desk duty in Norfolk, the Navy said. In a news release, officials said Borchers and Bruce-Ross were not suspected of misconduct themselves but were dismissed because they apparently lacked the ability to command.
"We hold our leaders to a high standard," Vice Adm. Harry B. Harris Jr., commander of the 6th Fleet, said. "Our nation expects no less and our sailors deserve no less."
The dismissed sailors, who have not been identified, were involved in fraternization, drunk and disorderly conduct and violation of orders while in port, the Navy said.
Capt. Dan Shaffer, head of Task Force 65, has been given temporary command of the Stout until a new commander arrives.