Footage released by GMP showed the car driving up onto kerbs, squeezing past buses and swerving in and out of traffic.
At one point it drove at speed through the car park underneath the Tesco store in Pendleton Way.
One woman was taken to hospital with minor injuries after the suspect’s car collided with her vehicle, and an officer suffered a hand injury when a stinger device used to stop the car was dragged, the force said.
“This level of driving is obviously extremely dangerous, and I’m thankful to report that no one was seriously hurt during this pursuit,” GMP Sgt Neil Molloy said.
“The reckless actions of this man put members of the public at risk, and we’re incredibly lucky that no-one suffered serious injuries as a result of his actions.
“Driving in this manner through built-up residential areas is completely unacceptable, and I am pleased that our officers acted swiftly and professionally to bring the incident to a safe conclusion, secure an arrest and seize the vehicle.”
A force spokesman said the suspect remained in custody on suspicion of dangerous driving, driving while disqualified, and failing to stop.