Eyewitnesses said police broke up a protest at a hospital in the capital, Harare. The health workers regrouped later but were prevented by riot police from leaving the hospital.
The protesters planned to present a petition to the government calling for "urgent action" to address the crisis in the public health system, which is crumbling from lack of medical supplies, equipment and drugs.
Meanwhile, the government mouthpiece Herald newspaper reported on Tuesday that cholera had killed 36 people since Friday in the town of Beitbridge on the South African border. It said that 431 people had been diagnosed with the highly infectious intestinal disease.
The Herald said the local hospital had cleared all its wards to make room for cholera victims but that there were not enough staff or equipment to cope. The newspaper reported 11 bodies "scattered all over the place" in the female wards because there was no room in the morgue.
Health workers had no idea about the situation in surrounding rural areas because lack of fuel and transport prevented investigations, it said.
Beitbridge is one of the regions busiest border crossings, with huge volumes of vehicles and people passing to South Africa to buy supplies that are impossible to find in Zimbabwe.
Even before the Beitbridge outbreak, more than 130 people had died from cholera, which is spread by contaminated food and water. The disease is thriving in Zimbabwe because there is no money to maintain the sewage and draining systems, to clear garbage or supply clean water.
Aid groups fear the outbreaks will worsen as the rainy season progresses and Médécins Sans Frontières has warned that 1,4-million people are at risk. MSF said patients were lying outside on the grass at Harare's infectious diseases hospital and the charity was putting up tents to cope.
Zimbabwe, which has one of the world's worst HIV/Aids pandemics, once had among the best healthcare systems in sub-Saharan Africa. But the country's economic meltdown has led to chronic shortages of food and fuel, and daily water and power failures.
President Robert Mugabe, in power since independence from Britain in 1980, blames Western sanctions for his country's extreme financial woes. But critics point to corruption and mismanagement under his increasingly autocratic leadership.
Meanwhile, Zimbabwe is drafting a constitutional amendment empowering Mugabe to form a unity government, the information minister said on Tuesday, despite the opposition's refusal to join a Cabinet.
The opposition Movement for Democratic Change (MDC) has said it will not join a unity government with Mugabe until all issues in power-sharing talks are resolved.
In the government's first public reaction to a decision by Morgan Tsvangirai's MDC on Friday not to join a power-sharing administration until a dispute over some Cabinet posts has been resolved, and the Constitution amended, Information Minister Sikhanyiso Ndlovu was quoted by state radio as saying:
"The state is currently drafting Constitutional Amendment Number 19, which will be gazetted soon after consultations with the two formations of the MDC."
The amendment would allow Mugabe to form a unity government.
Tsvangirai has accused Mugabe of trying to take control of the most powerful ministries and freeze out his party in violation of a September 15 power-sharing agreement seen as the best hope of rescuing Zimbabwe's economy.
Ndlovu said Mugabe was still in the process of assembling a new Cabinet, but he and the Zimbabwe Broadcasting Corporation (ZBC) gave no timetable on when it would be announced.
"He [Ndlovu] urged the public to be patient as the process of forming a government is a process and not an event," the ZBC said. - Sapa-AP, Reuters