Local officials said that this week's heavy rains had already claimed 66 lives, injured 111 people and displaced 17,000 people.
At least 19 people died in Mozambique, according to the government, while a further 24 perished in Zimbabwe, state-owned Zimbabwe Broadcasting Corporation reported. "There were people inside", he told AFP, saying they were listed as missing.
The ministry of information said the Zimbabwean national army was leading the rescue efforts.
Joshua Sacco, a member of Parliament in the eastern district of Chimanimani, told Reuters that the storm had left a trail of destruction reminiscent of Cyclone Eline in February 2000, which devastated southern Zimbabwe.
Cyclone Idai has affected more than 1.5 million people in the three southern African countries, according to the United Nations and government officials.
One school has been shut in the area and students were waiting to be airlifted to safety.
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.
"We need state intervention on a massive scale to avoid biblical disaster", MDC spokesman Jacob Mafume wrote on Twitter.
Weather experts feared the cyclone which brings heavy rains and high winds could have resulted in more flooding particularly in the lower Shire River districts of Chikwawa and Nsanje which are now recovering from last week's floods.
A major cyclone the equivalent of a strong Category 2 hurricane approached the coast of Mozambique late Thursday, prompting residents to brace for what weather authorities have called a likely "worst case scenario".
"The situation is dire but we don't know the exact particulars", said Jamie LeSueur, the Red Cross's roving emergency operations manager for Africa, who was making the 1,200-kilometre (745-mile) trip from Maputo to Beira by road after flights were cancelled and the airport closed.
Authorities were forced to close Beira global airport 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 aircraft are damaged".