Wayne Bvudzijena, assistant police commissioner, said on state television that the march had been banned over fears it would escalate into violence and looting.
"We are not going to allow this march and we are going to use all the powers entrusted in the police to stop it," he said.
The MDC announced last week it would demonstrate against the crumbling economy and call for a new constitution which it said would guarantee that elections in March would be free and fair.
Morgan Tsvangirai, leader of the MDC, and several other senior opposition figures were beaten up by the police when they tried to stage a mass protest last year.
"The government is totally bereft and bankrupt of any capacity to govern this country. This government has failed"
Tendai Biti, MDC secretary general
Tsvangirai said earlier this month that his party might boycott the elections unless the government implemented the new constitution.
Mugabe, who has led Zimbabwe since its independance in 1980, is blamed for the country's economic crisis.
Unemployment is at 80 per cent and food scarcity very high.
The country's official annual rate of inflation is at 8,000 per cent, but some economists believe it is 50,000 per cent.
John Makumbe, a political analyst and Mugabe critic, said the ban on the mass protest was predictable.
"This is a government which fears street protests, and they have a record of never taking chances," Makumbe said.
"With what is going on in Kenya, I did not expect they were going to allow that to go ahead even for good marks on their political record."