Kennedy was selected by the Detroit Red Wings in the fourth round (80th overall) of the 1988 National Hockey League (NHL) Entry Draft. His first professional season was split between the Red Wings in the NHL and their minor league affiliate Adirondack Red Wings of the American Hockey League (AHL). At the NHL level, Kennedy scored two goals and added seven assists in 20 games. Kennedy spent the next four seasons bouncing between the AHL and NHL within the Red Wings organization. The Winnipeg Jets acquired Kennedy from the Red Wings after the 1993–94 season. The NHL lockout meant that Kennedy did not actually play for the Jets before being picked up on waivers by the Calgary Flames. Kennedy spent two seasons in Calgary, then the Flames decided not to renew his contract in 1996, shortly after his sexual abuse revelation. He signed as a free agent with the Boston Bruins for the 1996–97 season but also spent time with the Providence Bruins, Boston's AHL affiliate. The 1996–97 season was Kennedy's last campaign in the NHL but he later resurfaced in the 1998–99 season with the Manitoba Moose of the now-defunct International Hockey League. Kennedy also played for EV Landshut of the Deutsche Eishockey Liga in Germany during the 1998–99 season.