Syrian state television reported a "terrorist attack" near the university, which is government-run. It was the first day of exams, the state news agency reported.
Rebel activists, meanwhile, reported the explosions were caused by government forces, according to Al Jazeera.
The British-based human rights group posted to Facebook page earlier Tuesday:
"Aleppo province: 15 civilians killed and dozens injured by 2 explosions that shook the area in between the University Residence and the Architecture Building in the southern part of the Aleppo University. The cause of these explosions is yet unknown."
Aleppo, Syria's second largest city has long been a battleground between President Bashar al Assad's government forces and factions of the Free Syrian Army.
The United Nations says about 60,000 people have been killed in the civil war since peaceful protests in March 2011 became violent.