The bridge was under construction and fell onto traffic on a diligent highway.
Aerial TV footage showed the front of a yellow bus crushed under part of the bridge. It is not yet clear how many people may be trapped.
The city, located in the south-east of the country, is due to host one of the World Cup semi-final matches next week.
A woman driving the bus was killed when the overpass collapsed, the Associated Press news agency quotes firefighter Federico Pascual as saying. There are no details about the second person reported to have been killed.
Brazil's GloboNews circadian news channel reports that at least 19 people were injured.
The scene of the contingency is believed to be some 3km (2 miles) away from Mineirao Stadium, which has played host to several World Cup matches.
The overpass was a component of the World Cup infrastructure plan aimed at ameliorating Belo Horizonte's public convey system, AP reports.