Honors showed "extremely poor judgment" in producing and starring in the crude comedy videos, Adm. John C. Harvey Jr., commander of U.S. Fleet Forces, said in a statement.
The captain was reassigned to an administrative role, the Navy said.
The videos were broadcast on the nuclear-powered aircraft carrier in 2006 and 2007. The videos, made while Honors was second-in-command, included gay slurs, mimicked masturbation and racy shower scenes. They came to light in The Virginian-Pilot newspaper over the weekend.
"The responsibility of the commanding officer for his or her command is absolute," Harvey said. "While Capt. Honors' performance as commanding officer of USS Enterprise has been without incident, his profound lack of good judgment and professionalism while previously serving as executive officer on Enterprise calls into question his character and completely undermines his credibility to continue to serve effectively in command."
Harvey said Capt. Dee Mewbourne would be permanently assigned as commanding officer of the Enterprise. Mewbourne most recently commanded the USS Dwight D. Eisenhower and has been serving as chief of staff for Navy Cyber Forces.
Earlier today, support poured out for Honors, with former sailors saying he should not be relieved over what they called morale-boosting videos.
Former Petty Officer Phillip Ciesla, who served on the Enterprise under Honors, said stripping the captain of his command would be an unfit punishment.
"I don't believe it's the right course of action," he said on CBS' "The Early Show." "He didn't do it out of malice or cruelty. He did it to entertain his crew and boost our morale."
He said the videos were taken out of context because they weren't made for the public. They were intended to amuse the sailors, who work long hours, halfway around the world, for months at a time, he said.
"They were meant for the crew only," he sad. "For our entertainment, lighthearted laughter. None of it was ever meant to be taken seriously."
But the Navy called them "not acceptable" and launched an investigation. The Navy has shifted away from the bad-boy behavior that came to light in the 1991 Tailhook scandal, in which women were assaulted during drunken revelry.
Still, the military did not immediately remove Honors.
A group that has advocated for gay service members praised the military for condemning the videos.
"What we see here is, unfortunately, a 49-year-old Navy captain acting like a 19-year-old fraternity boy," Aubrey Sarvis, executive director of the Servicemembers Legal Defense Network, told The Washington Post. "There is no place for that type of frat-house behavior."
A Facebook page supporting Honors had more than 6,000 followers this morning. And a female sailor who served on the Enterprise from 2007 until September also praised him.
Another former sailor, Pete Clarke, also said the videos were made for sailors and were something that civilians could not understand. He said relieving Honors of duty would be unfair.
He noted that at first, the Navy downplayed the videos, but then condemned them.
"Which Navy are we talking about?" Clarke, a family friend of Honors, said on NBC's "Today" show. "I think the political correctness at the Pentagon needs to be checked on this.
"It's a shame that videos from four years ago are going to affect a heroic person."
But Harvey said the Navy holds its officers "to a higher standard."
"Those in command must exemplify the Navy's core values of honor, courage and commitment, which we expect our sailors to follow," he said.
"Our leaders must be above reproach, and our sailors deserve nothing less."