Flooding in region affected by the storm had already killed more than 60 people.
Air force helicopters were rescuing people, but flights were being slowed by the heavy winds, media reports said.
President Emmerson Mnangagwa has declared a State of Disaster in respect to areas in Manicaland province that were affected by Cyclone Idia, which has claimed 31 lives and displaced 200 people, a lot of them in Chimanimani and Chipinge. "There were people inside", he told the AFP news agency, saying they were listed as missing. Around 100 houses had been swept away in Ngangu township in Chimanimani town, he said.
Meanwhile a spokesman for Zimbabwe's opposition Movement for Democratic Change party, Jacob Mafume, tweeted that a "serious humanitarian crisis" is unfolding in the country's eastern districts.
There have been emergency relief camps opened, with President Peter Mutharika declaring a national emergency.
At least 43 people died in central Mozambique and Zimbabwe after a tropical cyclone tore through the southern African nations, knocking out electricity and phone networks and cutting power to South Africa from a hydropower dam.
Authorities in Mozambique said heavy rains before the cyclone struck had already claimed the lives of 66 people, and displaced a further 17,000.
They had also affected neighbouring Malawi, where 56 people died and almost a million others were affected, the government said. The storm hit with wind gusts of about 160 kilometres per hour, causing ocean waves of up to nine metres high.
"We have compatriots suffering without hope and we have to restore hope", he said on Friday as he set off on a three-day state visit to the kingdom that was previously known as Swaziland.
This was revealed by Acting President Retired General Constantino Chiwenga when he sent a message of condolences to the affected families following the cyclone disaster that has so far claimed 31 lives and left over 100 unaccounted for.
"The situation is now dire and we are calling for emergency both locally and internationally", said Madiro, who is also the Zanu-PF provincial chairperson for Manicaland.
When the cyclone hit Mozambique, authorities there were forced to close the worldwide airport in the port city of Beira after the air traffic control tower, the navigation systems and the runways were damaged by the storm. "Houses and trees were destroyed and pylons downed", an official at the National Institute of Disaster Management (NIDM) told AFP.
"The runway is full of obstacles and parked aircrafts are damaged".
The storm also affected power supplies to neighbouring South Africa which imports electricity from Mozambique to supplement its own production.
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