Floods destroyed roads and bridges in several regions of the state. The storm also triggered landslides and the partial collapse of a dam at a small hydroelectric power plant. A second dam in the city of Bento Goncalves is also at risk of collapsing, authorities said.
In Porto Alegre, the capital of Rio Grande do Sul, the Guaiba river broke its banks, flooding streets.
Porto Alegre's international airport has suspended all flights for an indefinite period.
State Governor Eduardo Leite told reporters on Friday evening that the death toll could still rise.
More rains could hit the northern regions of the state on Saturday, according to Brazil's National Institute of Meteorology, and authorities urged people living in areas at risk to seek shelter elsewhere.