Five officers received minor injuries in the "quick-moving" incident on Tuesday afternoon, police said.
A 49-year-old man has been arrested and will face multiple charges in court today.
Wellington District Commander Superintendent Corrie Parnell said police were called to Trinity Ave at 5.25pm after a report of suspicious behaviour.
Supt Parnell said a vehicle of interest was seen leaving the area, but officers signalled for the driver to stop.
"It [the car] did not stop and instead, drove into the police vehicle and then into two other police vehicles that arrived to assist.
"A member of the public's vehicle was also hit by the man's vehicle. Thankfully the member of the public was uninjured."
The driver then fled on foot, but was arrested soon afterwards.
Supt Parnell said five police staff had been assessed for minor injuries, and three police vehicles sustained significant damage.
"Our staff go to work every day to help make our communities safer, and behaviour such as this where police staff and vehicles are targeted is unacceptable," Supt Parnell said.
"I am incredibly proud of the work from our staff in this quick-moving event where a vehicle was used as a weapon against Police, creating a massive risk to the safety of everybody involved."
The arrested man will appear in the Hutt Valley District Court on Wednesday, facing three charges of aggravated assault, a charge of indecent assault and failed to stop for police.
Supt Parnell said further charges had not been ruled out.
