The fatal collision happened on Stockwell Road in Lambeth, south London, at around 11.20pm on Wednesday.
The Metropolitan Police said the marked car was responding to a 999 call at the time of the incident.
The pedestrian was treated by paramedics, but died at the scene.
Her next of kin have been informed.
The police force said the incident has been referred to the Directorate of Professional Standards and the Independent Office for Police Conduct, which has launched an investigation.
Road closures remain in place and traffic is being diverted away from the area.
Several surrounding streets have also been shut, including Brixton Road, Stockwell Road and Landor Road.