At issue is an allegation of an inappropriate relationship, a U.S. military official told CNN.
Capt. John R. Nettleton has been temporarily reassigned to a post in Jacksonville, Florida, the Navy said in a statement released Wednesday.
The Navy did not say why, withholding further details "due to an ongoing NCIS (Naval Criminal Investigative Service) investigation."
But a U.S. military official said that in the course of investigating the death of a civilian, the Navy received information alleging that Nettleton was engaged in an inappropriate relationship with the civilian's wife.
According to the Miami Herald
, Christopher Tur was found dead in the waters off Guantanamo Bay on January 11. He had been a worker at the base commissary.
Having an affair violates military law -- the Uniform Code of Military Justice -- and could in itself constitute grounds for Nettleton's reassignment.
There are initial indications that Tur's death was a suicide, but no cause of death has yet been determined, according to one official with knowledge of the situation.
Defense Secretary Chuck Hagel was asked about the story by reporters at the Pentagon on Thursday. He confirmed that Nettleton was no longer in command, but had no further comment.
"Well, the base commander has been relieved," said Hagel. "It is now in the purview of appropriate authorities. So, I won't have anything to say specifically about that, which would be inappropriate. But the commander has been relieved and that is right."
The Naval commander at Guantanamo Bay does not oversee the detention facility that President Barack Obama has vowed to close.
Nettleton has been in charge since June 2012.
The decision to relieve him of his duties was made by Rear Adm. Mary M. Jackson, commander of Navy Region Southeast, the military said in a statement.