The search and rescue agency said in a statement on Thursday that the bus driver lost control shortly before the crash in an area near the city of Sumedang in West Java.
The ministry said the bus was carrying high school students and some parents. There were 39 survivors.
Photos on the spot showed that the bus had reached its side, and rescue workers were looking for more victims.
Supriono, an official of the local search and rescue agency, later said the evacuation efforts had been completed and the survivors had been taken to a nearby hospital.
The exact cause of the accident was not immediately clear, although the ministry said there were initial indications that the vehicle’s technical tests were out of date.