Mugabe appears increasingly intolerant of criticism
But before they could set off, riot police sealed off the campus and started to beat them up.
Students said they had wanted to march peacefully to hand in their petition, which denounced army indiscipline and called for the resignation of President Robert Mugabe.
The latest violence came as the United States joined the chorus of international condemnation of Mr Mugabe's government.
Resignation call
The student protest came in response to the death over the weekend of student Lameck Chemvura, who was thrown from a train by a soldier.
Reports quoted witnesses as saying the soldier had accused him of being a supporter of the opposition Movement for Democratic Change (MDC).
The angry students said they were calling for Mr Mugabe to resign because as commander of the defence force he was clearly failing to impose any discipline.
They said reports that a soldier had been arrested for Mr Chemvura's murder were irrelevant, given the "lack of control at the highest level".
Unconfirmed reports say one student was arrested during the clashes, but our correspondent said many student leaders had now fled underground.
The spiralling violence has also left a white farmer in critical condition in hospital in Harare.
Farmer Alan Bradley was shot over the weekend by unidentified assailants who had used branches to block a road to his farm southeast of the capital.
Many farm workers and white farmers have been injured, and some killed, in an often violent campaign of invasions of white-owned farms in the past 18 months.
US anger
On Monday, the United States joined global condemnation of Mr Mugabe, rejecting the government's use of the word "terrorist" to describe a group of foreign journalists.
"The statements reflect a continuing trend of harassment of the free press by the government of Zimbabwe," US State Department spokesman Richard Boucher told reporters.
"The United States rejects any comparison between the international coalition's fight against terrorism and the deterioration of the rule of law and the state-sponsored violence that has emerged in Zimbabwe," he added.
Sanctions
It appears that Zimbabwe could be moving closer towards some form of sanctions following a warning from the the British Foreign Office not to harass foreign correspondents based in Bulawayo.
A presidential spokesman was quoted in the government newspaper as calling six journalists "terrorists" after they reported on last week's political violence in Zimbabwe's second city, Bulawayo.
Also on Saturday, The Herald quoted President Robert Mugabe as rejecting calls from a visiting European Union delegation to monitor next year's presidential elections.
The EU has threatened to impose sanctions against Harare if it is not allowed to monitor next year's elections, in which Mr Mugabe will face his strongest-ever challenge from the MDC's Morgan Tsvangirai.
EU officials earlier said that relations were "critical".