Police say the incident occurred after officers responded to an alarm at Peter Easton's Pub on Cookstown Road in St. John's around 5:20 a.m. Friday.
They say a suspect was inside, but left the building and jumped into a vehicle parked nearby.
An officer tried to stop the vehicle, but it drove off and dragged her to a nearby intersection where she managed to break free.
Her injuries are reported as not life-threatening.
Police say they're asking for the public's help in finding 30-year-old Gordie Anthony Bishop.
Bishop is facing charges including aggravated assault of an officer and assaulting an officer with a weapon.
He's described as about 5-foot-10 with brown hair and blue eyes.