The collision took place at around 10.50am on London Road between Carmyle Avenue and Westhorn Drive.
The constable had been responding to a separate report of a broken down vehicle when he was struck by a Vauxhall Corsa.
The officer has been taken by ambulance to the Queen Elizabeth University Hospital for treatment.
He is understood to have sustained serious leg injuries.
A spokeswoman for Police Scotland said: "We received a report of a man being struck by a vehicle around 10.50am.
"Emergency services are in attendance and a section of the road has been closed."