Officers were following the car bearing stolen number plates through Ascot in Perth's east about 1am on Thursday when it came to a stop.
As they tried to detain the three occupants, one officer was hit by the car and dragged underneath.
His colleagues were forced to lift the car off him and attempted CPR at the scene before he was rushed to hospital in critical condition.
Three people are in police custody and an investigation is under way.
Police Minister Paul Papalia said the 28-year-old constable, who is relatively new to the force, was in intensive care with his family at his side.
"It's a very, very worrying situation at the moment," he told reporters.
"This is something that every single police officer will feel ... in particular, those officers that were at the scene and responded and resuscitated their colleague.
"It's an incredibly hard, challenging incident and I feel for them all."
Police Commissioner Col Blanch attended the hospital overnight and met with the other officers involved in the incident.
Detectives remained at the scene near Ascot Racecourse on Thursday.
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