Among the victims, five were from the same family travelling by car in the capital Belo Horizonte metropolitan region on Tuesday.
A landslide buried their car which carried a couple, their three and six-year-old children and another relative, Xinhua news agency reported.
The rains intensified over the weekend, causing major flooding and landslides, along with the isolation of municipalities due to flooding.
Total 145 out of 853 municipalities of the state decreed an emergency situation, while over 17,000 people have been displaced.
Several rivers in the Minas Gerais state are overflowing due to the large amount of rainfall, and there is a danger that some dams may overflow.
Since the beginning of the rainy season in October, at least 19 people have been killed in the state.