South Yorkshire Police said in a statement that emergency services were called to reports of a collision on the A57 between Moss Way and Coisley Hill in Sheffield at around 8.15pm on Monday.
It said: “A marked BMW 3-series police car was responding to an incident and travelling towards Coisley Hill when it collided with a silver Citroen C3, travelling in the opposite direction.
“The 46-year-old officer driving the police car, was sadly pronounced dead shortly after the collision. He was responding to an immediate incident at the time.
“A 61-year-old Sheffield woman, who was a passenger in the Citroen was taken to hospital but passed away shortly after,” it added.
A 63-year-old man, who was driving the Citroen, was taken to hospital where he is in a serious condition.
Assistant Chief Constable David Hartley said: “On behalf of the force I’d like to offer my sincere condolences to all of those left bereaved by this terrible tragedy.
“We are doing everything we can to support them through this difficult time. I ask that their privacy is respected at this sad time.
“We have lost a friend and a colleague from our police family in this incident.
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“The officer has been with us for 12 years and was a passionate, professional and universally liked officer. His colleagues, and everyone across the force, are devastated by what has happened.
The Independent Police Complaints Commission (IPCC) is investigating the incident.