The US coastguard in Miami said a British Royal Navy helicopter hoisted a woman and two children from the overturned vessel on Thursday.
A distress call had been sent from the boat on Wednesday, stating it was disabled and adrift in seas and facing 20-foot waves and 100 mph winds.
The man has not been named and the coastguard said his body has not been recovered.
US coastguard footage shows three people stranded on the capsized vessel and desperately waving for help before being winched to safety.
Maria has barrelled across the Caribbean over the past few days, claiming the lives of at least 19 people so far, with many others missing.
A hurricane warning was issued for the Turks and Caicos islands, as the eye of the category three storm approached the British overseas territory, the US National Hurricane Centre (NHC) said.
With winds of up to 125mph predicted, the NHC said a “gradual weakening is forecast during the next 48 hours” as Maria moves past the east of Turks and Caicos on Friday.
The NHC said a “dangerous storm surge accompanied by large destructive waves” could raise water levels by up to 12ft in the overseas territory, with an isolated rainfall deluge of up to 20ins.
As the hurricane rolled through the region it skirted past the overseas territories of the British Virgin Islands and Anguilla, which were left devastated by Irma.
Brigadier John Ridge, second in command of the UK’s Joint Task Force, said early reports suggested little new damage had been caused by the second major hurricane in two weeks.
“It is a huge relief that those two islands have not suffered as we had suspected they might do, and more importantly planned for - we planned absolutely for the worst,” he said.
“But we are not counting our chickens.”
With Maria having ravaged both Dominica and Puerto Rico, in the wake of the widespread destruction Mr Ridge said they had had a request for help in undertaking assessments.
Initial reports from Dominica suggest large-scale devastation, with 90% of buildings damaged or destroyed by the storm which made landfall with the island on Monday.
Also hitting Puerto Rico, it was the strongest storm in more than 80 years to sweep across the country - flattening homes and plunging the island into darkness after taking down power lines.
Mr Ridge said they took a “split team of half-civilian, half-military” into Dominica on a Chinook helicopter on Wednesday following the request.
“We have done that assessment and there are a number of nations involved in the response for it,” he said, adding that Maria has almost “completely destroyed their agricultural sector”.
He said the relief effort in Dominica was being co-ordinated by the Caribbean Disaster Emergency Management Agency (CDEMA) - with shelter, food and water being the critical aid requirement.
International Development Secretary Priti Patel described the situation across the region as an “unprecedented crisis”.
“Our focus now is on making sure the islands affected have the right supplies in the right places to deal with the aftermath of the latest hurricane,” she said.
So far, the Government has pledged more than £57 million towards the disaster relief.
A Red Cross appeal, boosted by the Department for International Development’s (DfID) aid match scheme doubling all public UK donations, has seen more than £2 million raised so far.
Ms Patel said: “The British public has once again shown its overwhelming generosity in a time of crisis by helping out the victims of hurricanes Irma and Maria.
“This money will ensure food, water and shelter goes directly to those who need it most on the worst-hit islands.”
More than 75 tonnes of DfID aid has already arrived in the region, which includes food, water, 3,000 shelter kits, more than 5,000 solar lanterns and 10,000 buckets.
Another 60 tonnes arrived on board HMS Ocean.