The university in Nigeria's north-eastern city of Maiduguri has closed because of the growing threat by the radical Islamist group, Boko Haram.
The BBC's Bilkisu Babangida in Maiduguri says the move follows strong rumours that the group plans to attack the campus.
Boko Haram opposes Western education and fights for Islamic rule.
In recent weeks, about 40 people have been killed in attacks blamed on the group.
On Tuesday morning, a bomb exploded near an army barracks in Maiduguri, with five casualties reported, our reporter says.
There has also been a blast at a church in the town of Suleja, near the capital, Abuja, correspondents say.
No casualties have been reported.
Last month, Boko Haram bombed the police headquarters in Abuja, killing at least six people.
Our reporter says Maiduguri, a Boko Haram stronghold, is gripped by fear with many people staying indoors.
Residents are worried that the military will carry out indiscriminate arrests as they search for the bombers, she says.
University authorities said they had closed the campus because of the growing insecurity in Maiduguri.
They urged students to stay at home under the protection of their parents.
Our reporter says students are packing up and leaving the campus.
Many of them come from other parts of Nigeria and their state governments have promised to help evacuate them from Maiduguri.
Last week, Maiduguri banned all motorbikes to prevent drive-by shootings by Boko Haram.
Boko Haram gunmen often use motorbikes to assassinate security officers and politicians.
The group's official name is Jama'atu Ahlis Sunna Lidda'awati wal-Jihad, which in Arabic means "People Committed to the Propagation of the Prophet's Teachings and Jihad".
But residents of Maiduguri, where it was formed in 2002, dubbed it Boko Haram.
Loosely translated from the local Hausa language, this means Western education is forbidden.
Residents gave it the name because of its strong opposition to Western education, which it sees as corrupting Muslims.