Cleveland Police said the incident occurred at 3.39am on Saturday near the South Bank area east of Middlesbrough and that all occupants of the two vehicles died at the scene.
A Volkswagen Passat was travelling the wrong way down the A66 and collided head-on with a police vehicle on the same road, police said.
"This tragic incident will be felt across Cleveland, within our communities and throughout the entire policing family," Cleveland police chief constable Victoria Fuller said.
The police force said it was still investigating the circumstances of the crash and was working to formally identify all the people killed.
A large white tent was erected over the scene, with multiple emergency service vehicles around.
Police have put into effect a drone exclusion zone around the site of the collision.
Local councillors David Taylor and Stephen Martin said in a Facebook post they were "deeply saddened" by the "unimaginable tragedy".
The incident will be reviewed by the United Kingdom's Independent Office for Police Conduct, as is common practice in such cases.
Following two recent head-on crashes near Dublin, one of which killed five people, Ireland's police chief this week warned that some young people were driving the wrong way on the motorway "for social media likes".
An Irish parliament committee has asked short-form video platform TikTok to explain how it removes content "that appears to glorify dangerous and illegal behaviour on our roads".
On Tuesday, Ireland's media regulator made a similar request.
with PA
