The accident happened around 2:00 p.m. at Linn and Main Streets.
Police say a Buick sped through a stop sign and rammed into a Mitsubishi.
The driver of the Buick got out of his car and sprinted from the crash.
A child in the other car suffered minor injuries and was treated at the scene.
"Anybody that flees the scene...of an accident where there is an injury involved stands a chance to face serious criminal charges," said Brad Kerns, an officer with the St. Joseph Police Department.
Police would not provide many details about the suspect, but say he is a white male.
Officers say they have a good idea of who the man is.