The Indianapolis Fire Department said the three fatalities were a husband and wife and a teenager who were among the passengers, The Indianapolis Star reported. The victims, who died at the scene, had not been identified, the newspaper said.
Another unidentified teenager who was among the injured was in critical condition, the Star said.
The newspaper said the bus, with 37 passengers and the driver aboard, was only about a mile from its destination when it crashed along North Keystone Avenue and fell over on its side.
The group was on one of two buses returning from a camp in Michigan.
Witnesses told authorities the bus was moving "at a high rate of speed'' as it rounded a turn from the Interstate 465 exit ramp onto Keystone, the Star said. The bus' brakes may have not worked properly, some witnesses said.
A motorist, Carol Albright, said she saw the bus "going very fast" when it hit a median dividing the southbound lanes of Keystone from the ramp to I-465.
"It kind of pivoted on the nose of the bus and did a little bit of a twist," she said. "How it didn't hit another car, I don't know."