The rough weather claimed the lives of 13 people in the northern province of Nampula and five in the central province of Sofala, local officials told Portuguese state television's African service.
The flooding cut several roads in Sofala, isolating thousands of people, and caused flooding in Beira, Mozambique's second largest city, they added.
Weather forecasters in the former Portuguese colony said the heavy rains, which began on December 25, were expected to continue over the coming days.
The torrential rains come in the wake of a lengthy drought that has left nearly one million people, mostly in the south of the country, in need of food aid.
In early 2000 floods caused widespread devastation in Mozambique, where the wet season lasts from November to March.