The road section, which was still under construction, gave way and crushed part of a bus, killing two and injuring a further 19, but further fatalities are possible as fire crews work to free a car still trapped underneath.
Belo Horizonte has hosted five World Cup games so far and is also the venue for one of the semifinals next week.
Police pic of collapsed viaduct in Belo Horizonte. Been here three weeks, have to say I'm not surprised. Very sad. pic.twitter.com/UOfLNrSKl4— Ben Hayward (@bghayward) July 3, 2014
The capital of Minas Gerais is also home to Argentina in this World Cup, with Alejandro Sabella's side based just 10 kilometers from the collapsed overpass.
The tragedy comes just one day after the daughter of a well-known Argentine journalist was killed in a car crash just outside the city.