A witness who saw part of the incident on Quay St said the driver "went on the footpath to get away from the cops".
"The vehicle was later observed travelling north on the Northern Motorway and Eagle continued to provide ground units with updates on its location," police said.
Shortly before 2.20pm, police say the vehicle rammed a police car on Knights Close in Rothesay Bay on Auckland's North Shore.
"A police officer has sustained injuries as a result and is being examined by paramedics, though the injuries are thought to be minor."
The driver is in police custody, and is likely to face charges.
Motorists have been told to avoid the area.
"Please use an alternative route until further notice. Expect some traffic delays in the surrounding area," Auckland Transport says.