The hostages were driven in lorries towards the mainly-Shia area of Sadr city after the armed men occupied all four floors of the building, put the women into separate rooms and handcuffed all the men, officials and eyewitnesses said.
It is unclear if all the hostages have been released, with some reports saying that up to 20 people may still be missing.
Several police officers from the al-Karradah district are being questioned over the incident.
Academics are increasingly being singled out in sectarian violence, and thousands of professors and researchers have fled from the country.
At least 155 education workers have been killed since the war began and a university dean and a Sunni geologist were murdered in recent weeks.
The security forces have been accused of participating in or ignoring several previous mass kidnappings which are believed to have been carried out by sectarian groups.
The Sunni minority have blamed many of the kidnappings on armed groups from the now-dominant Shia parties, who control the interior ministry.
The higher education ministry is headed by a member of the main Sunni Arab political bloc.