Garde has the Impact currently in the seventh and final playoff position in the Eastern Conference, with the club holding a record of 10 wins, 13 losses and four draws.
“Because I have so much respect for Remi as a person and as a professional, it was a very difficult decision to make and it was well thought, but our latest series of failures in the past couple of months and the way the team acts on the field led to that change,” Impact president and CEO Kevin Gilmore said in a club release.
“We hope to bring back confidence to this group of players for the last stretch of the season, to get a playoff spot and to perform in the Canadian Championship final."
Garde, who has also managed Lyon and Aston Villa, was named Impact manager in November 2017. In the 2018 season, his first in charge of Montreal, Garde led the team to a seventh-place finish in the Eastern Conference which, based on the playoff format last year, was the final spot out of the postseason.
Overall, Garde led the Impact to a record of 24 wins, 29 losses and eight draws in MLS regular season action.
In Garde's place comes Cabrera, who was only fired by Houston last week.
Under Cabrera, the Dynamo struggled in 2019 after a hot start, and the Colombian couldn't survive a run of two wins, 11 losses and one draw in the Dynamo's 14 matches leading up to his firing.
Overall, Cabrera posted a record of 32 wins, 39 losses and 22 draws in MLS play as head coach of the Dynamo.
The Impact also announced that assistant coach Wilfried Nancy and goalkeeper coach Remy Vercoutre will remain with the club, while Patrice Bernier will also join as an assistant coach.
Meanwhile, assistant coach Joel Bats and fitness coach Robert Duverne will not remain with the Impact.
Montreal became the sixth MLS club to sack their head coach this season, following FC Cincinnati (Alan Koch), Colorado Rapids (Anthony Hudson), New England Revolution (Brad Friedel), Real Salt Lake (Mike Petke) and the Dynamo.