The Interfax news agency cited an unnamed "informed source" as saying the evacuation of the plane had been delayed by some passengers insisting on collecting their hand luggage first.
TASS news agency, citing a source, said at least one person was killed.
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Russia's Investigative Committee said two children were among the dead but did not immediately provide further details. In total 78 people were onboard, 37 of them survived, including four crew members. Passengers evacuated using the aircraft's emergency slides.
The plane had taken off from the airport bound for Murmansk, but turned back after encountering unspecified problems in the air.
According to Markovskaya, 28 passengers are now in the airport terminal, five have been taken to hospital.
A screengrab of a social media video shows a fire of a Russian-made Superjet-100 at Sheremetyevo airport outside Moscow.
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It was reported that the fire could be caused by lightening strike.
According to the play-back of the flightradar data, made by Bloger51 in Murmansk, the plane was in the air for 27 minutes. The plane apparently did not have time to jettison fuel before the emergency landing, news reports said.
Russia's Investigative Committee has launched a criminal probe into the incident, it said on its website.
The plane's manufacturer, Sukhoi Civil Aircraft, said the plane in Sunday's accident had received maintenance at the beginning of April.
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"Through the twisted metal, rescue workers are trying to get to the last rows of seats, where there may be additional victims", a source told the Interfax news agency.