Tedi Sutardi, an Indonesian navy officer, on Tuesday said there was no food and water on board the boat and all the survivors were in very poor health.
"They were drifting for about 21 days," he told AFP. "Most of them are in critical condition and are receiving treatment at a local state hospital in East Aceh district.
He said the survivors were still being interviewed by Indonesian authorities, but communication was difficult.
Last month Indonesian fishermen found another group of about 170 Rohingya drifting off Sumatra. Many of them had severe injuries they said were the result of beatings from the Thai military.
| Rohingya migrants have claimed abuse at the hands of the Thai and Mynamar military
Myanmar's military rulers effectively deny citizenship rights to the Rohingya, a Muslim minority who live in the west of the country.
Human rights groups say the Rohingya face systematic discrimination and abuse by Myanmar authorities, leading hundreds to try to flee the country by boat every year.
Rather than finding refuge though, many say they have found even more abuse at the hands of the Thai military who have been accused of beating boatloads of migrants before pushing them back out to sea, often without food or water, and in boats with engines removed.
Rights groups say hundreds may have perished at sea.
The Thai government has rejected allegations of abuse, and says the Rohingya are economic migrants seeking a better life, not refugees fleeing persecution.
Forced to convert
The latest group of Rohingya found off Sumatra on Tuesday said they had left their homes in Myanmar's western Arakan state after being forced to convert to Buddhism.
Al Jazeera correspondent Step Vaessen reporting from Jakarta said navy officials found the survivors, one of whom was 13 years old, to be very weak after their ordeal and said it was a miracle they had survived.
The boat was so small that some of the group had been forced to stand.
She said there were also clear signs that they had been beaten, and the Indonesian authorities are now trying to decide what to do with them.