McCrimmon, the newly appointed coach of the Lokomotiv Yaroslavl ice hockey team, and Demita, who played for part of 16 seasons with five NHL teams, were among those killed, the Kontinental Hockey League club confirmed.
McCrimmon, 52, played 18 years in the NHL and had spent the past three seasons as an assistant coach for the Detroit Red Wings.
Other recent NHL players such as Ruslan Salei, Karel Rachunek, Josef Vasicek, Karlis Skrastins and Alexander Vasyunov also died in the crash.
The Yak-42 aircraft was traveling to Minsk, Belarus, when it crashed and burst into flames soon after taking off, RIA Novosti reported.
The team was flying to Minsk to open the Kontinental Hockey League season Thursday against Dinamo Minsk. Officials said it wasn't immediately known which team members were on the plane.
Hockey player Alexander Galimov and flight crew member Alexander Sizov survived the crash and were hospitalized in grave condition at a hospital in Yaroslavl, Interfax reported. The burn unit director said burns covered 80 percent of Galimov's body and Sizov sustained bone fractures and "torn wounds."
"Passenger body parts were found in the Volga River, where part of the fuselage fell," a police source told RIA Novosti.
Russian President Dmitry Medvedev, scheduled to participate in a political forum in Yaroslavl Thursday, offered condolences to the families of the victims. His press secretary said Medvedev would visit the crash site.
The Russian Emergency Situations Ministry said 37 passengers and eight crew members were aboard the plane.
KHL President Alexander Medvedev said authorities would work to ensure Yaroslavl, about 160 miles northeast of Moscow, had top-drawer hockey.
"I want to reassure you that we will do everything possible to make sure hockey of the highest level continues in Yaroslavl, and that Lokomotiv remains one of the KHL's strongest clubs," Medvedev said in a televised statement.
The team won the Russian championship in 1997, 2002 and 2003 and placed third in the KHL last year.
Russia's Investigative Committee and the Interstate Aviation Committee both began investigations into the crash.