A cause of death was not given.
Klima became the unlikely Oilers hero when he ended the longest game in the history of the Stanley Cup Final with a triple-overtime goal in the series opener against Boston after spending long stretches of the contest on the bench.
"Klima helped the Oilers win the 1990 Stanley Cup while scoring a memorable triple-overtime winner in Game 1 of the Final," the NHL said in a statement. "Our sympathies are with his family, friends and many fans."
Klima played for the Detroit Red Wings, Oilers, Tampa Bay Lightning, Los Angeles Kings and Pittsburgh Penguins.
In 786 NHL games across 13 seasons, Klima scored 313 goals and added 260 assists.