McKay was selected by the Detroit Red Wings in the sixth round, 113th overall, of the 1985 NHL Entry Draft. He split the 1987–88, 1988–89 and 1989–90 seasons between the Red Wings and their affiliate in the American Hockey League (AHL), the Adirondack Red Wings. McKay stuck with the Wings in the NHL for the 1990–91 season, appearing in 47 games. While showing a scoring touch in the AHL, McKay only scored 4 goals in 83 total games with the Red Wings and was unable to find consistent playing time. Following the season, McKay and Dave Barr were sent by rule of an arbitrator to the New Jersey Devils as compensation for the Red Wings' signing of free agent Troy Crowder. The deal did not work out for the Wings as Crowder only played in seven games for the team before incurring a serious injury. McKay developed into a solid third and fourth line player that the Wings would later covet in the latter part of the decade. It was a move that Red Wings senior vice president Jim Devellano resisted at the time and regretted later.