The team and family did not announce the cause of death, but Skinner had been in declining health, said Eddi Chittaro, chairman of the Windsor/Essex Sports Hall of Fame in Windsor, Ont.
The group inducted Skinner in 2006, and he spoke briefly at the awards ceremony.
"He coached with the likes of Gordie Howe and all the great teams they had back in the '50s," Chittaro said. "He was still mentally sharp. He had lots of great stories."
The Stanley Cup that Detroit won in Skinner's first year as coach was the team's seventh. The Wings were 123-78-46 under him.
Skinner was born on Jan. 12, 1917, in Selkirk, Man.
After a minor league playing career, he coached the Windsor Spitfires before the Red Wings made him their head coach for the 1954-55 season, after Tommy Ivan left to coach the Chicago Blackhawks. Skinner coached the team through 38 games of the 1957-58 season, when the Wings replaced him with Sid Abel.
Skinner then held a variety of management jobs with the club, including scouting and farm team development. He was general manager from 1980-82, when Mike Ilitch bought the team.
"It's a big loss to the Red Wings," said longtime Detroit left-wing Marcel Pronovost, who skated for Skinner as a junior player for the Spitfires in 1947-49 and later as a member of Detroit's 1955 NHL championship team.
"He was good with the kids," Pronovost said.
Far from being an autocratic boss, Skinner relied heavily on his captains and other veteran team members, Pronovost said from his home in Windsor.
"He was very much dependent on the older players on the team," said Pronovost, who played for the Red Wings from 1949-65. "He worked them as a family."