Syahrial, a local disaster official, says the group was discovered on the rickety boat by fishermen on Tuesday about 3 kilometers (1.8 miles) off the coast.
Syahrial, who goes by a single name, said it wasn't clear where they traveled from or where they were heading.
An outbreak of violence that began in 2012 prompted thousands of Rohingya to flee Myanmar by sea to Thailand, Malaysia, and Indonesia.
Syahrial said the men, ranging in age from 14 to 28, were weak from hunger and dehydration after a 15-day voyage. They were brought ashore and admitted to a navy shelter house in East Aceh district.