The crash happened at 2:20 p.m. on a day when the central London museum is usually teeming with pedestrians including international tourists. Photographs showed a dented silver car and a man being pinned to the ground outside the museum.
Police said Saturday they are working to establish the circumstances and the cause.
The London Ambulance Service was responding to the incident.
Police said more details would be released later. There was no immediate statement on the number or severity of the injuries.
London's official terrorist threat level has been set at "severe," indicating an attack is highly likely.