British media reported a car had mounted the pavement outside the tourist attraction.
Police described the incident in the South Kensington area of west London as a collision and said the motive for the incident was under investigation.
"Inquiries to establish the circumstances and motive are under way," police said.
The museum said on Twitter it was working with police after "a serious incident" outside and would provide more information later.
The police statement said officers were on the scene and that London Ambulance Service had been called. The Ambulance Service said it was responding.