No one was hurt, but a window at the nearby Crossroads Trading Co. store was shattered by gunfire. The store is also managed by the University Book Store.
The university sent out an alert shortly after 2 p.m. informing students and staff members of the incident at 4326 University Way NE.
Police said a black Audi fled from the scene, and officers stopped the vehicle a short time later in the 4300 block of Lake Washington Blvd.
Video from AIR 4 showed a man at the scene of the traffic stop being handcuffed and placed into the back of a patrol car.
It was not clear what prompted the shooting.