"Up until now we have counted at least 20 dead in landslides that buried houses in the district of Gakenke," the ministry's spokesman Frederic Ntawukuriryayo told AFP.
"Most of the victims were children," Ntawukuriryayo added, without specifying how many were minors.
The landslides occurred at the peak of Rwanda's rainy season, affecting homes on hillsides and in valleys.
"It's a huge catastrophe," the spokesman said, adding that rescuers had managed to pull some survivors out of the disaster area.
But "this year, the incidents and number of victims is rising," said Ntawukuriryayo, blaming the El Nino weather phenomenon.
At least 67 people have been killed in such incidents across Rwanda from January to April this year, 12 of them on a single night in the suburbs of the capital Kigali, where 1,500 homes were damaged during rainstorms.