The 60-year-old led the club to the Campeonato Brasileiro Serie A title in 2012 - his first full season in charge since taking over from the sacked Muricy Ramalho.
However, a run of poor results this year have seen Fluminense flirt with the league's relegation places, while the Rio de Janeiro side have lost their last five outings.
And that dreadful form has prompted club president Peter Siemsen to terminate Braga's contract.
In the meantime, the club's youth coachs are expected to oversee Fluminense's upcoming meeting with Cruzeiro.
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