The Muslim refugees from Burma were found by Indonesian fishermen on Sunday.
It is not clear where they were heading, but they are believed to have left Burma a week ago, police say.
The Rohingya are not recognised by the military-backed government in Burma, and hundreds of thousands have fled in recent years.
The UN says they are one of the most persecuted minorities in the world.
According to police reports, the refugees had no food or fuel when they were found.
Djadjuli, the police chief in Aceh Besar, told the BBC there were 5 children and 5 women among the group of 74 Rohingya Muslims.
He added that when the group was first rescued, the children were sick from dehydration but that their condition has since improved.
This is the latest boatload of Rohingya Muslims to arrive in Indonesia, the BBC's Karishma Vaswani in Jakarta reports.
Thousands of Rohingyas have been fleeing communal violence in western Burma.