Reports say another boat was turned back by the Indonesian navy.
The fate of another vessel of stranded migrants off the coast of Thailand is unclear after it was towed out of Thai waters.
Human Rights Watch has warned of deadly "human ping-pong" in the Andaman sea, where thousands more are believed to be adrift, struggling to land.
Rohingya Muslims have been leaving Buddhist-majority Myanmar, also known as Burma, because they are not recognised as citizens of the country and face persecution. Many of the Bangladeshis at sea are thought to be economic migrants.
Critically ill
They attempt to flee every year during the non-monsoon season, but the smugglers who take them to Thailand have been scared by a recent Thai crackdown and instead they are reported to have been abandoned at sea.
"For more than two months we were in the boat, we were only given little food and we were beaten when we asked for more," said Mohamad Ali, a Bangladeshi migrant.
He told the BBC that he had paid 12,000 Malaysian ringgit ($3,366; £2,133) to the boat's captain for his passage.
An Indonesian police chief in Aceh told AFP news agency that he believed the rescued boat had already been pushed out of Malaysian waters by Malaysia's navy. He said it was sinking and towed to shore by fishermen. Medical officials said eight of the migrants were critically ill.
