The 20ft seas and 115mph winds capsized their vessel, with the extreme weather delaying rescue efforts by the US Coast Guard and a Royal Navy helicopter.
Dramatic footage from the US Coast Guard showed a woman and two boys standing on the hull of their overturned boat, the Ferrel, wearing life jackets and waving to rescuers.
A coastguard plane and rescue helicopter from the British Royal Fleet Auxiliary Mounts Bay ship were deployed to the scene near Vieques.
“Coast Guard watchstanders received an alert via emergency position indicating radio beacon and then a distress call on 20 September from the Ferrel stating they were disabled and adrift in 20-foot seas and 100-knot winds,” a spokesperson said.
Radio contact was later lost but a Hercules aircraft spotted the vessel and communicated its position to rescuers.
A woman and two children were hoisted to safety by the Royal Navy but a man was reported dead inside the capsized vessel.
The US Coastguard said the conditions made it “inaccessible to search and rescue crews”.
The commanding officer of RFA Mounts Bay, Captain Steve Norris, said: “My ship and crew demonstrated exceptional teamwork today to save these lives, and I am immensely grateful to them all for their efforts in this operation.
”It is with regret that we understand that a fourth individual at the scene is missing, presumed dead. Our thoughts go out to their family at this difficult time.“
The man was British and had been on board the Ferrel with his two 12-year-old children and their Dominican mother, the Sun Sentinel reported.
The survivors, who have not been named, were placed on the USS Kearsarge.
The force-five hurricane left a trail of destruction through Puerto Rico and Dominica and is moving towards the Turks and Caicos Islands.
It has flooded towns, crushing homes and killed several victims, with millions on Puerto Rico facing weeks without electricity after the storm knocked out the entire grid supplying 3.4 million people.
Maria's death toll across the Caribbean has climbed to at least 32, mainly in Puerto Rico and Dominica.
Its most recent classification was a strength of three, with maximum sustained winds near 125mph, but gradual weakening is expected during the next two days.
Maria is the third major hurricane to hit the Caribbean this month and the strongest storm to make landfall in Puerto Rico in almost 90 years.
More about: #HurricaneMaria