Police were following the Citroen before the crash.
It was believed firefighters had been working to release a woman who had become trapped in one the vehicles.
Multiple ambulance services were on scene after receiving a call around 10am to help with the fire service and the police.
Some witnesses at the scene have stated, They saw the Citroen being followed around the East Marsh before the crash happened.
A lot of people were gathered around the scene as emergency services worked to release a person from the red car.
It is believed a woman was removed from the red car and paramedics treated her on the roadside before she was put in to a ambulance which was waiting at the scene.
Witnesses have said they believe one man was arrested at the scene of the crash.
A Humberside Police spokesman said: “A man has been arrested following a road traffic collision on Wellington Street in Grimsby this morning.
“A silver Citroen collided with a red Chrysler around 9.50am. A woman who was in the Chrysler has been taken to hospital after being cut out of her car. It’s believed she doesn’t have serious injuries.
“The arrested man who had been driving the Citroen suffered minor injuries was taken to hospital for checks.”
A Humberside Police spokesman said: “A police car had been following the Citroen at low speed before the collision occurred, after officers observed the driver acting in a suspicious manner.
“Surrounding roads have been closed off while emergency crews are in attendance and recovery takes place. Log 146 of 10/4/19 refers.”
More details to follow when known.