The crash happened in the early hours of Saturday morning near South Bank, Middlesbrough.
Cleveland Police said a Volkswagen Passat carrying five people was travelling the wrong way along the A66 when it collided with the police car.
Two police officers were inside the marked vehicle, which was travelling in the correct direction at the time of the collision.
All seven people in the two vehicles were pronounced dead at the scene.
A major emergency response was launched following the crash, with 14 units from the North East Ambulance Service attending. The response included ambulance crews, a specialist paramedic, a hazardous area response team and a doctor from the Great North Air Ambulance Service.
"Sadly, despite the best efforts of everyone attending, a number of patients died at the scene," an ambulance service spokesperson said.
The section of the A66 where the collision occurred has been closed while investigators examine the scene.
A large white tent has been erected over the crash site and a drone exclusion zone has been introduced around the area.
The Independent Office for Police Conduct (IOPC) is investigating the circumstances surrounding the collision because a police vehicle was involved.
IOPC director of investigations Nicola Marfleet said investigators had been sent to the scene to begin reviewing evidence.
"This is a tragic incident, and my thoughts are with family and friends and all those affected, including the emergency services in attendance," she said.
Cleveland Police Chief Constable Victoria Fuller said the force was supporting the families of those who died.
"No one should leave their home and not return safely, including police officers serving their communities and protecting the people of Cleveland," she said.
The fatal collision comes amid renewed concern in Ireland about vehicles being driven the wrong way on motorways.
Earlier this month, five teenagers died when a car travelling in the wrong direction on the M9 in Co Kildare collided with another vehicle, seriously injuring four members of a family. The incident followed a separate M50 collision on 9 August in which nine people were injured after a car was driven the wrong way.
Investigations into the A66 collision and the recent Irish crashes are continuing.
