Homicide detectives were called in when the woman in her 50s succumbed to her injuries at the emergency room of the Peter Lougheed Centre.
A woman who arrived at the hospital with the victim at about 4 a.m. was taken into custody, police said.
Officers later surrounded a house in the 5800 block of Memorial Drive N.E. and cordoned off the back alley, including a Ford truck, which they said is connected to the incident.
Detectives detained a man associated with the truck for questioning, officials said.
Neighbours in the area told CBC News a couple in their 50s lived in the house.
A nearby residence is also being examined, police said.
Investigators also taped off the hospital emergency room while they interviewed witnesses.
An autopsy is scheduled for later on Friday.