Student sources said the protests began Thursday after authorities posted notices saying students who had not paid tuition fees would not be allowed to take exams starting Monday.
Many students find it hard to pay fees now set in U.S. dollars or other hard currencies.
The sources said about 1,000 students marched toward the administration office but were stopped by riot police who arrested 30 students and beating many protesters.
Ten students remained in police custody Friday and two were hospitalized, sources said.
Spokesman Blessing Vava of the Zimbabwe National Students Union described the melee at the university in an interview with VOA reporter Patience Rusere.