Coast Guard officials tweeted that the three were from Cuba. They told officials their boat had capsized in rough waters and they were able to swim to the island.
The trio told the crew they had survived on coconuts, conchs and rats, news outlets reported.
It was not immediately clear whether they were migrants attempting to come to the United States, or if they were just lost at sea, U.S. Coast Guard Petty Officer 2nd Class Brandon Murray told the South Florida SunSentinel.
They were taken to the Lower Keys Medical Center, where none appeared to have serious injuries.
“I cannot recall a time that we saved people who were stranded for over a month on an island,” he told the newspaper. “That is a new one for me.”