The car was later found abandoned on Hamilton Rd in Papatoetoe about 12.35pm.
"Inquiries led police to a nearby address on Tui Rd where the woman was taken into custody around 1.05pm," Pirret said.
The woman is likely to face a number of charges in connection with the incident, including unlawfully taking a motor vehicle.
The police car had minor damage but no police property was missing.
The firearms remained secured in the car during the incident.
"This is a concerning incident involving an offender, who has taken extremely reckless measures to avoid being detained," Pirret said.
"Thankfully the police officer, whose vehicle was stolen, was not injured during the incident, but they are understandably shaken and will be supported."
Pirrett commended the officer for acting fast to arrest the woman and recover the stolen car.
An investigation into the incident and review of police procedures would now take place, while the Independent Police Conduct Authority will also be notified.