It says they apparently committed suicide.
They were the first reported deaths among the suspected terrorists held at the base for up to four and a half years without being charged.
Two men from Saudi Arabia and one from Yemen were found "unresponsive and not breathing in their cells" early on Saturday, according to a statement from the Miami-based U.S. Southern Command, which has jurisdiction over the prison.
Attempts were made to revive the prisoners, but failed.
One defence official, who requested anonymity, said that initial reports were that two of the detainees hanged themselves while the third suffocated or choked himself.
Pentagon officials said the three men were in Camp 1, the highest maximum security prison at Guantanamo, and that none of them had tried to commit suicide before.
That camp was also the location where two detainees tried to commit suicide in mid-May, when a riot broke out at the facility.
Then the two men, who took overdoses of an anti-anxiety medication they had hoarded, were found and received medical treatment and have since recovered.
The United States is holding about 460 men at Guantanamo Bay on suspicion of links to al-Qaida and the Taliban, which has become a sore subject between President Bush and his allies.
Bush, spending the weekend at Camp David, was notified of the incident. The State Department was consulting with the governments of the home countries of the three prisoners, whose names were not released.
The military said in its statement that "all lifesaving measures had been exhausted" in the attempt to revive the detainees.
The remains were being treated "with the utmost respect," and a cultural adviser was assisting the military.
Though the military termed the deaths suicides, the Naval Criminal Investigative Service was investigating to establish the official cause and manner of death.
A UN panel said on May 19 that holding detainees indefinitely at Guantanamo violated the world's ban on torture.
The panel said the United States should close the detention centre.
There also has been a hunger strike among detainees since August.
The number of inmates refusing food dropped to 18 by last weekend from a high of 131.
The military has at times used aggressive force-feeding methods, including a restraint chair.