The incident occurred at the Slavyansky Bulvar metro station in the west of the city.
15 people were also injured in the crash, police told local media.
Cops are at the scene and the driver has been detained.
Horrifying footage shows the bus driving down the passage as helpless pedestrians are crushed underneath.
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Bus ploughs into crowd at Moscow underground station

Other CCTV shows the vehicle slowly approaching the station after navigating past parked cars.
10 ambulances and three medical helicopters have been dispatched and the Mayor of Moscow is reportedly at the scene.
Pictures show hundreds gathering round the station as emergency services rush to treat the injured.
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The driver tried to apply the brakes but they did not function, investigators claim.
A preliminary examination showed he was sober during the crash, local media report.
The crash happened in icy conditions and an inspection of the entire Moscow bus fleet has now been ordered.