"We lost 31 Zimbabweans," the ministry of information published Twitter on Saturday, adding that people were "shaded" in a flood that consumed dozens of homes and caused massive damage to the infrastructure.
The National Civil Protection Unit runs a rescue operation, with the help of Red Cross officials in Zimbabwe and the International Organization for Migration.
Forty people have gone missing, the government said.
Speaking to the local media, Karikoga Kutadzaushe, director of operations at the Red Cross in Zimbabwe, said the situation was "quite tragic", adding that people displaced by devastation need immediate shelter. The Ministry of Information of Zimbabwe announced on Saturday that "two command centers" were created to deal with people saved from the worst areas.
The town of Ngangu in Chimanimani and the Rusitu Valley community were the hardest hit, officials said.
Films published in social media show extreme floods, destroyed homes and blocked vehicles.
Apparently the Zimbabwean president Emmerson Mnangagwa shortened his state visit to the United Arab Emirates to make sure he was "directly involved" in the national response. He declared the state of the catastrophe in the affected areas, the ministry of information tweeted.
The official spokesman for the government called it "a serious humanitarian crisis".
Cyclone Idai landed in Mozambique on Thursday, according to the World Meteorological Organization. This has affected tens of thousands of people throughout the country and neighboring Malawi.
The UN Office for the Coordination of Humanitarian Affairs (OCHA) said on Saturday that although the impact has not yet been determined, preliminary reports point to "loss of life and significant damage to infrastructure".
UN officials estimate that severe floods have affected 1.5 million people in Mozambique and Malawi, where it has reportedly killed over 120 people.