The ministry of information said the Zimbabwean national army was leading the rescue efforts.
The World Meteorological Organization said that although the storm is now weakening, it has affected "tens of thousands" of people living there as heavy rain is expected to pelt the country over the next several days.
Two of the victims were students who died when a boulder hit their school, causing the wall of the dining room to collapse on top of them, the state-run Zimbabwe Broadcasting Corporation said. Elsewhere in Chimanimani, 13 Zimbabwe Consolidated Diamond Company (ZCDC) staff in Mawenje who moved to the mountain are waiting for rescue teams, while 67 houses have been damaged in Chipinge leaving at least 5 families homeless in the district.More news: Trump fails to end 'Apprentice' contestant's defamation lawsuit
Zimbabwe's opposition Movement for Democratic Change spokesman Jacob Mafume tweeted that a "serious humanitarian crisis (is) unfolding" in eastern Zimbabwe districts. "There were people inside", he told the AFP news agency, saying they were listed as missing.
"We need state intervention on a massive scale to avoid biblical disaster", he said.
Mozambique has been struck by severe cyclones in the past, including Eline in 2000, when 350 people died and 650,000 were displaced across the wider region.
They had also affected neighbouring Malawi, where 56 people died and almost a million others were affected, the government said. Roads were flooded and the airport was shut down.More news: Kylie Jenner Reveals The Name She ALMOST Picked For Daughter Stormi!
Describing it as a "difficult emergency" to tackle, he told AFP said it would require "the full force of the humanitarian community behind the government of Mozambique to respond to rapidly".
South Africa's military has sent in aircraft and 10 medical personnel to help in Mozambique and Malawi, it said in a statement on Saturday.
An official at the National Institute of Disaster Management (NIDM) told AFP earlier that "houses and trees were destroyed and pylons downed".
The low lying city of Beira was the worst hit by Friday's cyclone, with Chinde to the north also taking a beating and communications with other villages along the coast severed by a 2-meter (6.5-foot) storm surge.More news: World reacts with sadness and anger to New Zealand mosque attacks
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