The Frenchman was only appointed in November on a three-and-a-half-year deal, but has been unable to prevent their slide towards relegation.
Villa sit bottom of the Barclays Premier League, 12 points from safety with seven games remaining.
Villa said in a statement on Tuesday night: "The club would like to place on record its sincere thanks to Remi for all his efforts during a difficult period and wish him well in the future."
Eric Black will take over as acting manager until Garde's replacement is appointed.
17 Norwich 28
18 S'land 26
19 Newcastle 25
20 A Villa 16
Garde, a former Lyon boss, won just two league games after taking over from Tim Sherwood. Villa have lost their last six and conceded 18 goals in the process.
They are nine points behind second-bottom Newcastle.
Garde was understood to be unhappy with his failure to be backed in the transfer market in January, with Villa opting not to sign a player despite his personal efforts.