"We lost 31 Zimbabweans," the Ministry of Information told Twitter on Saturday, adding that people were "taken away" in floods that took dozens of homes and caused great infrastructure damage.
The Civil Protection Unit of the country manages rescue, with the help of the Red Cross of Zimbabwe and the International Organization for Migration, officials say.
There were 40 people missing, the government said.
Speaking to local media, Zimbabwe Red Cross Director Karikoga Kutadzausha said the situation was "quite terrible," adding that people displaced by devastation were in immediate need a shelter. The information ministry in Zimbabwe announced on Saturday that "two command centers were established" to take over those who were saved from the worst areas.
The city of Ngangu in Chimanimana and the Rusitu Valley community were the hardest hit, officials said.
Videos posted on social media show extreme floods, ruined homes and stuck vehicles.
Zimbabwe's President Emmerson Mnangagva has reportedly shortened his state visit to the United Arab Emirates to ensure it is "directly involved" in the national response. He declared a state of disaster in the affected areas, the Ministry of Information announced.
The government's official spokesman called it a "serious humanitarian crisis".
Cyclone Idai made a slide in Mozambique on Thursday, the World Meteorological Organization said. She hit tens of thousands of people across the country and neighboring Malawi.
The UN Office for the Coordination of Humanitarian Affairs (OCHA) announced on Saturday that although an impact has yet to be established, initial reports indicate "loss of life and significant damage to infrastructure".
UN officials say heavy floods hit 1.5 million people in Mozambique and Malawi, where more than 120 people were reportedly killed.