The bus was travelling on an overpass by the city of Joao Monlevade when a collision with a tractor-trailer sent it careering off the side of the road, before plunging 45 feet and landing on train tracks.
Footage on social media showed smoke billowing from the crash site as emergency service workers attended the scene.
According to state police, there were 45 passengers on board the bus, 26 of whom were sent to nearby hospitals with at least three sustaining life-threatening injuries.
Two of the passengers left in critical condition were children, lieutenant Pedro Aihara, spokesperson for the Fire Department of Minas Gerais, told the local press.
"The health status of these three shows a very serious health condition. Most of them have a picture of traumatic brain injury, all of them are intubated and suspected of pneumothorax," Mr Aihara told Radio Itatiaia.
One person who was on board before the crash, thought to be the driver, has not been located by police.
Governor of Minas Gerais, Romeu Zema, called the incident a "tragedy" and said he stood in "solidarity" with friends and relatives of the victims.
"Teams of firemen, police, ambulances and helicopters are on site to assist the wounded, support families and investigate the facts," Mr Zema wrote on Twitter after the crash.
Localima, the company the bus was registered with, expressed “regret and deep sadness for the victims and their families”.