The crash was reported on eastbound lanes just before 11 a.m. near Malki Road, according to California Highway Patrol traffic logs.
The CHP says the Greyhound with 33 people on board was traveling in the second lane about 60 to 65 mph when a left front tire blew out.
The bus lost control, skidded left and hit a Mitsubishi Outlander in the next lane, then struck the center divider.
Authorities say one person on the bus suffered major injuries and another 11 were transported to a local hospital with minor injuries.
The remaining passengers were transported to the Morongo Tribal Hall in Cabazon. Nobody was injured in the Mitsubishi.
One lane was blocked on the eastbound 10 as authorities continued to investigate the accident.