The crash occurred around 3:30 p.m. near Loma Drive and Third Street.
The bus caused minor damage when it rolled backward into the wall, and the three passengers and driver were sent to the hospital with minor injuries, authorities said.
Metro issued a statement, saying the bus operator was fixing a mechanical issue outside his bus when the bus rolled back. About 15 to 20 people were onboard at the time.
The Los Angeles Police Department is investigating the incident.