The incident was reported just before noon on Exposition Boulevard near Watt Way, according to the Los Angeles Fire Department.
Two people on the USC shuttle were seriously injured and were transported by ambulance to a local hospital, fire officials say. They were awake and talking and considered to be in stable condition.
Sixteen passengers on the Metro train had injuries that were less severe but required treatment at local hospitals.
At least 37 people were treated and released on scene.
"This is what we call walking wounded," said LAFD Capt. Adam Van Gerpen. "They were able to walk off the train. We set up triage areas where our paramedics and EMTs were able to evaluate them."
Officials say there were more than 150 onboard the Metro train.
"I got thrown from my chair to the other chair," said Arlene Hayes, a passenger on the Metro train. "My whole left side is sore."
The cause of the crash remains under investigation.
According to a statement from Metro, the USC shuttle bus crossed into the path of the southbound Metro E Line train at Watt Way and Exposition Boulevard.
"Metro offers its sympathies to those injured during this accident," said the agency in the statement.
The front portion of the bus appeared to have significant damage, while the train's front windshield was cracked.
Exposition Boulevard was closed in both directions between Figueroa and Bill Robertson Lane. Metro said it's currently single tracking between 23rd St. Station and Vermont Station until further notice.
A bus bridge was also set up to help Metro passengers get through the area as the damaged train remained on the tracks.