The professor of agriculture, who was not identified, and the bomber died about 12:45 p.m. (09:45 GMT) just outside the university's gate, police spokesman Abdul Karim al-Jbouri said.
Less than an hour later, police found a second bomb, in another parked car about 230 meters (250 yards) away, and safely detonated it. The car was empty, al-Jbouri said.
The wounded included four university students and two police officers, he added.
Mosul is 360 kilometers (225 miles) northwest of Baghdad.