The losses were most concentrated in the state capital, Belo Horizonte, with 13 dead, according to the latest numbers.
Some 33,000 people have been displaced or evacuated from their homes, rescue workers said.
Last week, Minas Gerais recorded the wettest 24-hour period since precipitation records began being kept 110 years ago, with accumulated rainfall of 172mm (6.8 inches) from Thursday to Friday, according to the government's meteorological agency Inmet.
Televised images on Tuesday showed collapsed houses and others that had been submerged in 2 meters (6.6 feet) of water, while residents continue to battle thick mud after heavy rain.
The flooding comes a year after rains allegedly contributed to the collapse of a tailings dam in the town of Brumadinho, also in Minas Gerais, killing more than 250 people in one of the world's worst mining disasters.
The National Mining Agency (ANM) alerted mining companies on Monday to carefully monitor their tailings dams through Friday due to the heavy rainfall.