The plane is understood to have had 65 passengers on board alongside six crew members.
Images which have emerged on Russian media show what appears to be debris from the plane in the snow. The Russian Transport Ministry was considering various possible reasons, including weather conditions and pilot error, Interfax said.
The Emergencies Ministry said it had sent crews to the crash site, in Stepanovskoye.
The Antonov AN-148 aircraft had gone off the radar soon after it left Moscow's Domodedovo Airport.
Flight 703 was en route to Orsk, a Russian city near the border of Kazakhstan.
Russian President Vladimir Putin "deep condolences to all those who lost relatives and friends in this disaster", his spokesman Dmitry Peskov said, according to Tass. Many witnesses have reportedly told the media that they saw a plane in flames falling from the sky.
The national Investigative Committee said on its website that it had opened a criminal case over alleged breach of aviation safety.
"Initial reports from Russian Federation blamed the crash on weather or human error, however, it was unclear how that measures up with claims that the plane "[fell] apart in the sky".
The An-148 regional jet, developed by Ukraine's Antonov company, has been flying since 2012, with a two-year break between 2015 and 2017 because of lack of parts.
The Russian-made plane had been bought by Saratov from another Russian airline a year ago.