Carbonneau started his hockey career in the Quebec Major Junior Hockey League with the Chicoutimi Saguenéens. After an impressive 182 points season with the Sagueneens, Carbonneau was drafted 44th overall in the 1979 NHL Entry Draft by the Montreal Canadiens. His strong play as a defensive forward helped the Canadiens to a Stanley Cup championship in 1985–86, followed by three Frank J. Selke Trophy wins in 1987–88, 1988–89, and 1991–92. In 1989–90, he was named the captain of the Canadiens, and led them to another Stanley Cup win in 1992–93 against Wayne Gretzky and the Los Angeles Kings. On August 19, 1994, he was traded to the St. Louis Blues in exchange for Jim Montgomery. He played there for one season before moving to the Dallas Stars. He won his third Stanley Cup in 1998–99 with the Stars. Next season, Carbonneau and the Stars reached the Stanley Cup Finals again but this time they lost to the New Jersey Devils. Carbonneau retired shortly after that.
Carbonneau was one of the more popular Canadiens; fans chanted "Guy, Guy, Guy!" whenever he touched the puck, much as they did for Guy Lafleur (with whom Carbonneau played from 1982–85) during his career. He was also one of the most admired Dallas Stars players. He took the ceremonial opening faceoff for the Stars when they played the Canadiens at the last game at the Montreal Forum.