Emergency services were called to the incident on Carmunnock Road, Castlemilk, at around 5.40pm on Tuesday.
Photographs show both cars badly damaged, with the police car on its roof and its front end smashed in.
Police closed off the road and diversions were put in place.
It is unknown if there are any serious injuries at this time.
A spokesperson for Police Scotland said on Tuesday night: "Officers are in attendance after a crash involving a police car and another car at Carmunnock Road, Glasgow, which happened at 5.40pm.
A Scottish Fire and Rescue Service spokesperson said: “We were alerted at 5.47pm on Tuesday, October 27 to an incident involving two vehicles on Lainshaw Drive, Castlemilk, Glasgow.
“Operations Control mobilised two appliances to the scene to respond alongside emergency service partners.”
More to follow.