Police say the driver in the crash on Saturday has been detained. Preliminary information indicated the driver lost control of the vehicle.
There were no immediate details on the severity of the pedestrians’ injuries.
The accident took place on Ilinka Street, about 200 metres (650 feet) from Red Square and Moscow’s famous GUM shopping arcade.
Russia is currently hosting the World Cup and Moscow is one of 11 Russian cities where tournament games are being played.
This item will be updated when more details emerge.