Russian state television says the plane overshot the runway after landing.
Details are still emerging, but images of the scene on Twitter appear to show a badly-damaged aircraft lying in several pieces across a major road.
Some reports say the aircraft caught fire.
Reports said there were between eight and 12 people on board the Red Wings Tupolev-204, flight number RWZ9268, which was landing at Vnukovo airport.
Images of the scene show the aircraft split into several pieces, with the cockpit on the road.
Four people were severely injured, emergency officials said.
The plane’s tail and cockpit had broken off but the fuselage was largely intact.
There were fire engines at the scene and smoke could be seen rising from parts of the wreckage.
The plane had arrived in Moscow from the Czech Republic, government officials said.
The incident is said to have taken place at Moscow’s Vnukovo airport.
The images on Twitter show a plane bearing the Red Wings airlines livery, with the tail and cockpit broken off but the fuselage largely intact.
There are fire engines at the scene and smoke can be seen rising from the wreckage.
Unconfirmed reports say the plane had arrived from the Czech Republic with around eight passengers and four crew on board. The plane was reported to be a Tupolev-204.
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