"I have lost confidence for him to lead effectively," said Adm. John C. Harvey Jr., commander of Fleet Forces Command in Norfolk, Va., when announcing Honors was relieved of command.
Harvey said Honors was being replaced because of "the inappropriate actions demonstrated in the videos," ABC News reported.
"Our leaders must be above reproach and our sailors deserve no less," he said.
Taking over as the aircraft carrier commander is Capt. Dee Mewbourne, who most recently commanded the carrier USS Dwight D. Eisenhower, Harvey said. Mewbourne will command the ship when it sails for a deployment to the Middle East in two weeks.
ABC reported Honors was reassigned to administrative duties at the Norfolk naval base. Honors recently took command of the Enterprise, a coveted assignment in the U.S. Navy, which has 11 aircraft carriers.
Harvey said the investigation into the videos would proceed and "look at all aspects of the production of the videos, to include the actions of other senior officers who knew of the videos and the actions they took in response."
Honors made the inappropriate videos -- which included sexual jokes, gay slurs, subordinates in drag and sailors simulating masturbation -- while second in command on board the aircraft carrier.
Excerpts from the videos and descriptions of their content were published Saturday by The (Norfolk) Virginian-Pilot. The videos were shown to the Enterprise crew while it was deployed in support of the wars in Iraq and Afghanistan in 2006 and 2007.
Cmdr. Chris Sims, a Navy spokesman, called the videos "inappropriate."
Some criticized Honors for the videos, but others have rallied to his defense, The Virginian-Pilot reported.
"This is very serious," said Eugene Fidell, a Yale University law professor and president of the National Institute of Military Justice. "After watching the videos, I don't see how he could stay. He runs a warship, not a fraternity house."
On a Facebook page set up for the captain's supporters, writers argued the videos were harmless and Honors was right to use humor to boost morale, the newspaper reported.
The Navy's quick condemnation of the videos and swift investigation drew praise from a prominent gay-rights group, The Washington Post reported.
"What we see here is, unfortunately, a 49-year-old Navy captain acting like a 19-year-old fraternity boy," said Aubrey Sarvis, executive director of the Servicemembers Legal Defense Network, which has advocated for gay military members. "There is no place for that type of frat-house behavior."