An overpass in the FIFA World Cup host city, located approximately five kilometres from Estadio Governador Magalhaes Pinto, was still under construction when it fell on Thursday.
It collapsed onto several vehicles on a busy road and left two people dead, with a further 19 reported to be injured.
"With sadness we learned of the collapse of the (bridge) in Belo Horizonte," Rousseff said.
"The government (is) available to the municipality of Belo Horizonte and authorities as necessary.
"In this moment of pain, I offer my solidarity to the families of the victims."
A statement from the local Belo Horizonte government confirmed that an investigation into the incident was under way.
"The municipality of Belo Horizonte deeply regrets the serious accident on the afternoon of Thursday, when part of the viaduct…under construction…collapsed, causing the death of two people, one being the driver of an additional bus…and injuries to 19 people," it read.
"Shortly after the incident, the city has mobilised its team of SAMU – Service Mobile Emergency – the municipal hospital and the city's civil defence coordinator for bail immediately and provide all necessary support to victims and their families.
"A technical committee of the municipal works and infrastructure, civil defence, Cowan, the company responsible for construction, and Consol, the company responsible for the project, was immediately summoned to make a survey of all data involving the occurrence (and) develop a careful diagnosis of the causes of the accident and determine the action to be taken."
Mayor Marcio Lacerda declared a three-day period of official mourning following the two deaths, as all events associated with the World Cup were cancelled on Friday.
"(I offer my) sorrow and sympathy to the victims and their families," Lacerda said.
"At present, the most important is to give all assistance and support to those who suffered the consequences of this terrible accident."
The build-up to the World Cup was dogged by construction disasters with a crane collapse having killed two workers at Sao Paulo's Arena Corinthians in November, while in Manaus a man working on the Arena Amazonia died after being hit by a crane.
In Sao Paulo in June - just before the tournament begun - another construction worker, who was helping to build the monorail system, was killed when a section collapsed.
Belo Horizonte is set to host a World Cup semi-final on Tuesday.
