He tried to grab the keys from the ignition when the driver made off with the officer stuck partially inside.
West Midlands Police say he managed to eventually jump free but was lucky to escape with minor injuries.
A 37-year-old man was later arrested on suspicion of assault but police have yet to trace the car.
The man has since been released under investigation pending further enquiries.
Police say the officer was joined by a female colleague as they approached a silver Vauxhall Astra in Lichfield Road, in Walsall, on Saturday.
However as they moved in to speak with the driver, the car lurched backwards and knocked a female officer over with the car's open door.
As the male officer leaned inside to try and grab the keys the car drove off leaving him half trapped.
The incident happened at around 2.40pm.
Police are appealing for any witnesses or anyone who may have any dashcam footage.
The vehicle, a Vauxhall Astra with the registration SE07XLV, has not been recovered.
Supt Kim Madill, from Walsall Police, said: "This is a shocking incident which occurred when officers were just trying to do their job.
" Fortunately, I’m pleased to say their injuries aren’t serious, but it could have been much worse and it’s completely unacceptable for our officers to be injured in the line of duty.
“I’d urge anyone who saw anything or anyone who has any information to get contact us as soon as they can."
A 28-year-old man, who was arrested at the scene on suspicion of obstructing police, was later released with no further action taken.
Anyone with information can contact police via Live Chat at www.west-midlands.police.uk between 8am and midnight or call 101 anytime.
Quote crime reference number 20WS/247495H/19.