Primeau was drafted third overall in the 1990 NHL Entry Draft by the Detroit Red Wings after playing two years with the Niagara Falls Thunder of the Ontario Hockey League (OHL). He split his first two professional seasons with Detroit and their then-American Hockey League (AHL) affiliate, the Adirondack Red Wings. He set career highs in assists (42), points (73) and plus/minus (+34) in 1993–94. He made his only Stanley Cup Finals appearance while with the Red Wings in 1995, losing in a sweep to the New Jersey Devils. Primeau held out after the club signed Igor Larionov and after playing for Canada in the 1996 World Cup of Hockey, Detroit traded him (along with Paul Coffey and a 1997 first-round draft pick, ultimately used to select Nikos Tselios) to the Hartford Whalers in exchange for Brendan Shanahan and Brian Glynn a few days following the start of the 1996–97 season.