The order came hours after a coalition of opposition parties said they would stage mass rallies across the country on Saturday to push for reform before elections due in 2018.
Anti-government campaigners vowed to defy the order and also appeal to the courts.
"These are the last kicks of a dying regime and we expected no better from them," Douglas Mwozora, spokesman for the Movement for Democratic Change (MDC) opposition party, told AFP.
An earlier protest ban in Harare was overturned by the courts last week, despite Mugabe vowing a crackdown on dissent and blasting judges for "reckless" rulings allowing previous rallies.
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In a notice in the state-run Herald newspaper, Harare police chief Newbert Saunyama said a ban would be imposed on the "holding of public demonstrations" for one month starting on Friday.
Hardlife Mudzingwa, spokesman for the pressure group Tajamuka (We are agitated), told AFP "We will not heed this unconstitutional declaration by the police."
Opposition to Mugabe's 36-year reign has grown in recent months with a surge of public demonstrations, triggered by an economic crisis that has left banks short of cash and the government struggling to pay its workers.
Two weeks ago, police detained scores of people including activists and bystanders following violent demonstrations in the capital.
Mugabe, 92, has often used used brutal force to silence his opponents, and at the weekend he warned the protestors they were "playing a dangerous game".
"Let the opposition parties and all those angling for chaos, mayhem and violent demonstrations be warned that our patience has run out," Mugabe said in an address to his party's central committee.
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