The fishing boat, carrying about 350 people of the Muslim Rohingya minority, has been refused entry to Thailand.
Those on board told the BBC the crew abandoned them and disabled the engine. They said the bodies of those who had died were thrown overboard.
Indonesia, Malaysia and Thailand have been turning away migrant boats.
Several thousand people are still believed to be stuck in boats off the coasts of Thailand and Malaysia.
Most are Rohingya Muslims who cannot go back to Myanmar, also known as Burma, where they are not recognised as citizens of the country and are regularly persecuted.
Some of those who are adrift in the Andaman Sea have been provided with food, water and medicine by the Thai navy.
It is not clear how many other boats are in a similar predicament.
Some boats containing migrants have been towed over to the Malaysian side of the border - where most migrants want to go - only to be taken back into Thai waters.
No-one wants them, the BBC's Jonathan Head says, and seeing them off the southern coast of Thailand, near Koh Lipe, that it is a "desperate sight" as they beg for food and water.
On one crowded vessel with a lot of women and children on board, our correspondent saw people drinking their own urine from bottles.
The migrants - including 50 women and 84 children - said they had been at sea for three months.
Their situation became critical when their crew abandoned them without a working engine six days ago anchored near the Thai-Malaysian border.
Phil Robertson, deputy director of Human Rights Watch's Asia division told the BBC: "They're [Malaysia, Thailand and Indonesia] playing a game of marine ping-pong not wanting to take in the Rohingyas.
He said it was necessary for the three countries to work together in rescuing them before they decide who is going to take responsibility for them.
"This is an urgent humanitarian crisis and the Thais and others seem to be taking a gentle stroll."
Myanmar's unwanted people
As many as 8,000 migrants from Bangladesh and Myanmar are believed by the International Organisation for Migration (IOM) to be stranded at sea.
People smugglers are reportedly refusing to land their boats because their usual route through Thailand has been disrupted by a government crackdown. It was launched after the discovery of dozens of bodies in abandoned camps along the land route.
A senior Thai official reiterated on Wednesday that Thailand, Malaysia and Indonesia would all continue to turn the boats away.
On Sunday and Monday more than 2,000 migrants arrived in Malaysia or Indonesia after being rescued or swimming ashore.
The journey the migrants take - from Bangladesh or Myanmar through the Bay of Bengal to Thailand or beyond - takes several weeks and has been made by Rohingyas for much of the last 10-15 years.
Their journeys have in some cases been further disrupted because they have in effect been held hostage by the people smugglers.
Myanmar migrants on a boat stranded for a week in the Andaman Sea with no food or water say 10 people have died, while some are resorting to drinking urine.