The 18-year-old Yak-42 passenger jet took off from Yaroslavl's city airport some 300 kilometres (185 miles) northeast of Moscow.
The plane began listing to the left only seconds into the afternoon flight and crashed about 500 metres away from the Tunoshna airport.
Initial reports said the jet may have hit a local radar antenna and the twisted wreckage of the aircraft lay buried in the Tunoshna River as divers searched for signs of life.
"According to the latest data, there were 45 people on board -- 37 passengers and eight crew. Forty-four people died in the crash and one person survived," a police official told the RIA Novosti news agency.
The local emergencies ministry said the jet was taking members of the Lokomotiv Yaroslavl ice hockey team to the Belarus capital Minsk to open the 2011-2012 season of the Kontinental Hockey League (KHL) on Thursday in a match against Dinamo Minsk
Later on Wednesday, the Swedish embassy in Moscow confirmed for the TT news agency that Swedish netminder Liv, 30, was among the victims.
“There were players from Sweden, Poland, Ukraine, the Czech Republic, Germany, Belarus, Latvia and other countries on the team aboard the plane," a source told Interfax, although the bulk of the players were Russian.
KHL President Aleksandr Medvedev said that all of Lokomotiv's players and staff except one unnamed survivor died in a plane crash near the city of Yaroslavl.
Liv, who won Olympic gold for Sweden in 2006, played last season in Russia with HK Sibir Novosibirsk before moving to Yaroslavl Lokomotiv in May 2011.
The three-time Russian champion club was founded in 1959 and last won the country's title in the 2002-2003 season.
The team has a strong national following and recently attracted several younger stars from the NHL.
Before moving to Russia, Liv played for HV71 in the top Swedish professional league, the Elitserien.
Liv was named Eliteserien Rookie of the Year in 2001 and helped the club to three Swedish national titles in 2004, 2008, and 2010. In 2008, he was awarded the league's Guldpucken, given to the league's Player of the Year.
He has been a member of the Swedish national ice hockey team since 2000 and was considered one of the top goaltenders in Sweden over the last decade.
"It's with great dismay that we've received this news. It's so tough...I can't talk about it any more," chair of HV 71 told Aftonbladet.
HV 71 club director Peter Eklund called the crash an "unbelievable tragedy".
"We were clinging to hope but now we find ourselves overwhelmed with grief. It's hard to understand such an incomprehensible tragedy. Our thoughts go out to Stefan's family," he told local news website Jnytt.se.