Maxime Sauvé was born January 30, 1990 in Tours, France and grew up in Boisbriand, Quebec. A product of the Quebec major Junior League where he played for both the Quebec Remparts and the Val-d'Or Foreurs, he was selected in the second round of the 2008 NHL Entry Draft by the Boston Bruins.
Sauvé made his professional debut in the American Hockey League for the Providence Bruins during the 2009-10 season, appearing in six games and scoring twice.
The following year Sauvé impressed, notching 21 goals in 61 American Hockey League games.
On March 11, 2012, Sauvé made his NHL debut with the Boston Bruins in a road loss against the Pittsburgh Penguins.
On April 3, 2013, Sauvé was traded to the Chicago Blackhawks in exchange for forward Rob Flick.