The incident happened on Tuesday about 10 a.m., along US 421 South in Greensboro.
The Highway Patrol said a trooper tried to stop a car clocked at 61 mph in a 35 mph zone around 9:50 a.m. on Vandalia Road near Randleman Road in Greensboro.
The vehicle did not stop despite the trooper's blue lights and siren, and a pursuit ensued.
The chase continued for several minutes onto Pleasant Garden Road and finally ended with a Precision Immobilization Technique (PIT.) on Joseph M. Hunt Jr. Expressway near Pleasant Garden Road.
NCSHP said the driver then pulled out a handgun, and the trooper fired his weapon, striking the driver.
The driver, identified as Kasandra Forbes, 36, of Greensboro, was rushed to a hospital where she was listed in critical condition. The trooper was not injured.
NCSHP identified the trooper as Zachary Bullard, a six-year veteran stationed in Troop D, District 2 (Guilford County). Bullard has been placed on administrative duty pending an internal investigation, which is agency protocol in any trooper-involved shooting.
Charges against Forbes are pending.
The North Carolina State Bureau of Investigation (SBI) is conducting an investigation. Agents were on the scene collecting evidence and conducting interviews, the SBI said.
All southbound lanes on US 421 have reopened at Pleasant Garden Road, Greensboro police said.