The stricken vessel of Muslim Rohingya were found drifting at sea off the coast of Aceh province with no food and fuel, a report by the Jakarta Post said.
Five of the refugees are woman and five are children, the Post report said.
"We moved them to a facility at the Krueng Raya Employment Training Center to wait for verification process by the International Organization for Migration and United Nations High Commissioner for Refugees," Aceh Besar Police Chief Djadjuli said.
The latest boatload of refugees adds to Indonesia's growing tally of Rohingya asylum seekers fleeing ethnic violence between Muslims and Buddhists in Myanmar's western state of Rakhine -- formerly called Arakan.
Tensions in Myanmar's Rakhine state periodically have flared over the past 50 years, since the military takeover in 1962.
During the 1980s, the junta declared Rohingya non-citizens and which remains their current status
Around 735,000 Rohingya live in Rakhine state's northern area close to the Bangladeshi border, as estimated by the human rights organization Arakan Project, funded by the National Endowment for Democracy.
Rohingya are related to the Chittagonian Bengali across the border and are distinct from the majority Buddhist population of Myanmar, who are of Southeast Asian origin.
Bangladesh has received the majority of Rohingya fleeing by land and thousands remain in crowded refugee camps near the border.
But more and more are fleeing by boat to other countries, including Indonesia as well as Malaysia.
In November around 60 suspected illegal migrants drowned after an overcrowded boat carrying them to Malaysia capsized off the Bangladeshi coast.
Local fisherman managed to rescue about 50 passengers before the ship went down in the Bay of Bengal near the border with Myanmar, Bangladeshi media said at the time.
Many Rohingya are prey to ruthless people smugglers whose vessels are unseaworthy.
One of the passengers rescued in November claimed passengers had paid middlemen $370-$620 for the voyage to Malaysia. If a passenger were to find a job in Malaysia, they were to pay another $1,850 to the middlemen, the passenger said.
Indonesia has had to separate Buddhist and Rohingya detainees in several refugee camps to avoid clashes, sometimes fatal.
Recently 8 Buddhist fishermen at an immigration detention center in Belawan, north Sumatra, died during a brawl that started over alleged sexual harassment of a female Muslim refugee, the Post reported.
At the immigration detention house near the city of Tanjung Pinang, in Riau Islands province, house warden Surya Pranata told The Jakarta Post that 59 Rohingya Muslims are being held in separate areas from 23 Buddhists.
"I warned them that if they violate the law, such as by killing someone, it would end their chances of being sent to another country," Surya said.
"They would violate human rights and become an enemy of everyone."