Officers signalled to the vehicle to pull over for a routine check on Williams St, Kaiapoi, about 1.30am, a police spokeswoman said.
The driver initially stopped but then drove away at speed.
The spokeswoman said the fleeing driver was travelling at speeds above the legal speed limit but not at "excessive" speeds.
The woman was stopped in Riccarton after police used road spikes.
The vehicle finally came to a halt at the intersection of Clarence St and Riccarton Rd.
The woman is due to appear in the district court on Friday for failing to remain stopped for police, dangerous driving and possession of an offensive weapon, which is understood to have been an axe.
Meanwhile, police also observed a suspicious vehicle on Moorhouse Ave at 1.43am on Tuesday and initiated a pursuit.
The police spokeswoman said the pursuit was immediately abandoned due to the manner of driving, and the investigation is ongoing.