The move comes a day after the government declared an emergency following the outbreak of the disease.
In a statement, the national police spokeswoman Charity Charamba urged members of the public to take heed of the ban as it would assist in alleviating the spread of cholera, but did not say how long the ban would last, Presstv Reported.
The main opposition leader Nelson Chamisa had planned to hold a rally on Saturday (September 15), where he may take a mock presidential oath, three weeks after President Emmerson Mnangagwa was inaugurated following a court decision to uphold his disputed election victory.
Chamisa visited clinics where cholera patients were being treated earlier on Wednesday, calling for a collaboration between city health officials and the government.
Health Minister Obadiah Moyo told a meeting of government departments dealing with the outbreak that more than 3,000 people had been infected by cholera and the disease had now spread outside the capital.
This is the biggest cholera outbreak since 2008, when 4,000 people died and more than 40,000 were treated for this disease, according to ministry of health data.