The attacks, which come as Iraq suffers a prolonged surge in bloodshed, took place less than two weeks before a parliamentary election that will be a major test for security forces.
Officials gave varying accounts of the bombing of Baghdad's Imam Kadhim University.
A police colonel said a suicide attacker entered the university before detonating their explosives, while another bomber and a gunman were killed by security forces.
An Interior Ministry official said the bombing took place at the entrance to the university, while a second bomber was shot dead.
The attack killed at least three people and wounded at least nine, officials said.
Iraq is hit by daily bombings and shootings that kill hundreds of people each month, but attacks targeting universities are relatively rare.
In Babil province, south of Baghdad, a car bomb killed three people and wounded four, while two more car bombs killed three people and wounded 26 in Al-Rumaitha in Muthanna province, further south.
Iraqis vote on April 30 in the first parliamentary election since American troops left the country in late 2011.
Violence has killed more than 460 people in Iraq this month and upwards of 2,700 this year, according to AFP figures based on security and medical sources.
SHI/SHI