Mounties in the Nunavut capital say they received a call early Sunday about two women fighting.
RCMP allege that when they arrived they found one woman directing her dog to attack another woman.
Police say attempts to tranquilize the animal failed and officers shot the dog because it was loose and continuing to be aggressive.
A 29-year-old woman suffered numerous dog bites and was taken to hospital.
Saata Koochiajuke, who is 23, faces a number of charges including aggravated assault, uttering threats and resisting arrest.
Police say the dog's owner had been previously warned about its aggressive behaviour.
They are asking anyone who may have witnessed the event, or who may have video recordings of it, to contact them.