The Antonov An-148 plane operated by the domestic Saratov Airlines was flying to Orsk, a city in the Urals, and crashed in the Ramensky district on the outskirts of Moscow.
Russian news agencies reported 65 passengers and 6 crew were on board and all were feared dead.
News agencies said witnesses in the village of Argunovo saw a burning plane falling from the sky.
A source from Russia's emergency services told Interfax that the 71 people on board "had no chance" of survival.
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"The president offers his profound condolences to those who lost their relatives in the crash," Putin's spokesman Dmitry Peskov said.
State television aired a video of the crash site, showing parts of the wreckage in the snow. Russia has seen record high snowfalls in recent days and visibility was reportedly poor.
The Russian-made plane was 7 years-old and bought by Saratov Airlines from another Russian airline a year ago.
Russian media reported that the emergency services were unable to reach the crash site by road and that rescue workers walked to the scene on foot. Emergency services said in a statement that over 150 rescue workers were deployed to the site.
The Russian transport minister was on his way to the crash site, agencies reported. The transport ministry said several causes for the crash are being considered, including weather conditions and human error.
The governor of the Orenburg region, where the plane was flying to, told Russian media that "more than 60 people" onboard the plane were from the region.
Prosecutors opened an investigation into Saratov Airlines following the crash.
Plane crashes are common in Russia, where airlines often operate ageing aircraft in testing flying conditions.
In December 2016 a military plane carrying Russia's famed Red Army Choir crashed after taking off from the Black Sea resort of Sochi, killing all 92 people on board.
The choir had been due to give a concert to Russian troops operating in Syria.
Pilot error was blamed for that crash.
In March 2016, all 62 passengers died when a FlyDubai jet crashed in bad weather during an aborted landing at Rostov- on-Don airport.