The uniformed officer, a 28-year-old woman, and a uniformed colleague were in Eglinton Place, Kilwinning, North Ayrshire, when the incident happened at about 1.30am on Tuesday.
They were on their way to help colleagues with an inquiry when a blue Ford Focus was deliberately driven at one of them.
The vehicle hit the 28-year-old woman and she suffered serious leg injuries.
She was taken to University Hospital Crosshouse in Kilmarnock for treatment.
Police are treating the incident as attempted murder and are appealing to the public for information as they hunt the driver, who fled the scene.
In particular, officers are asking for anyone with dashcam footage of the area at the time of the incident to get in touch.
Detective Inspector Stephen McCulloch of Saltcoats CID said: “Our thoughts are with the constable, her family and colleagues and we continue to offer them all the necessary support.
“This incident is being treated as attempted murder and we will use all tools at our disposal to trace the person responsible.
“Anyone with information which might be relevant, who may have seen the car since or was driving in Kilwinning town centre in the early hours and has dashcam footage, is urged to get in touch.
“Information can be provided to Police Scotland via 101, quoting incident 0217 of 22 June, or anonymously to the independent charity Crimestoppers on 0800 555 111.”