The Continental Hockey League confirmed the death of the 52-year-old McCrimmon, who was in his first year as head coach of the Lokomotiv team.
McCrimmon was drafted by the Bruins as a defenseman in 1979 and played three seasons in Boston among his 18 years as a player in the NHL. He also played for Philadelphia, Detroit, Hartford and Phoenix. McCrimmon was most recently an assistant coach with the Detroit Red Wings.
"It's shocking. I think everybody in the hockey community is probably in shock and numb, myself included," Red Wings general manager Ken Holland said. "I've known Brad going back to the late '80s when we acquired him here. He was a real popular player. Then we had him as an assistant coach here. He loved hockey. He was a tremendous guy and wonderful family man. Our thoughts and prayers go to his wife Maureen and two children.
"Our thoughts and prayers go to everybody who had family on that plane. This affects the entire hockey community. It's a real sad day for the hockey world."
Barry Smith, who won five Stanley Cups as an assistant coach and also coached several years in the KHL, said he had spoken to McCrimmon about the league.
"Before Brad McCrimmon went over he came to see me to ask about what to expect," said Smith, who currently coaches in Switzerland. "I mentioned to him how difficult travel was because of all the time zones. Brad was really excited about the opportunity to be a head coach. It's really sad."
Smith added that he flew the on the same type of airplane when he was in Russia.
"But I must say Lokomotiv is one of the better organizations in the KHL," Smith said
McCrimmon was drafted by the Bruins 15th overall in 1979. He roomed with fellow rookie defenseman Ray Bourque during the 1979-80 season in Boston. In his three seasons with the Bruins, McCrimmon totaled 54 points.
ESPN.com's Pierre LeBrun contributed to this report.