A witness at the scene tells TMZ ... Matt was driving his Ford Escape out of a Mobil station near the USC campus Saturday night around 8:20 PM ... when he collided with a bicyclist.
We're told the rider was knocked off the bike ... and Matt immediately stopped the car to check on the man.
Sources say one of the bike pedals was lodged in the bumper of Matt's ride ... but the two men were able to pry the part from the car.
After a quick conversation, we're told both men decided it wasn't necessary to call police ... and went their separate ways. We're told the biker did not appear to suffer any serious injuries.
We called both USC and Barkley's family about the story -- so far, no comment from either.