Emergency services have been at the scene since just after 10am and the A52 is closed at the junction with Mareham Lane, with traffic being diverted by road blocks at the A15 Osbournby roundabout and at the Swaton crossroads.
Officers warned that the road will be closed until around 5.30pm this evening to allow a thorough investigation due to the police involvement.
A force spokesman said: “The incident, which involved a police car and another car, has resulted in minor injuries to the two officers and the driver of the other vehicle. All have been taken to hospital for treatment.
“The police car was responding to an emergency call when the incident happened.”
They added: “Investigations are ongoing and anyone who was in the area or who has dashcam footage is asked to contact Lincolnshire Police on 101 quoting incident number 111 of June 16.
“Please avoid the area if possible.
“A further update will be provided when the road is clear.”
Google Maps are reporting a build up of slow moving traffic and congestion either side of the Threekingham crossroads as well as at both sides of the road closure and on lanes where the traffic has been diverted, such as the B1177 to Billingborough, the B1394 to Helpringham and on Mareham Lane.
Residents reported that drivers were exceeding speed limits down the country lane through Threekingham to try to avoid the blockage.