Jean Claude Twishime, spokesman for the Ministry of Disaster Management and Refugees, said landslides killed 15 people in Karongi district. He said two more people were killed in flooding and another was struck by lightning on Monday.
He said some people are still missing.
The landslides have washed away houses and destroyed farmland in Karongi and the nearby Rubavu district, AP reported.
Heavy rains and lightning strikes have been frequent so far this year in Rwanda, a country of many hills.
Since January the Ministry of Disaster Management and Refugees has recorded 183 deaths and 215 injuries related to bad weather.