Another woman was taken to hospital with serious, potentially life-threatening injuries.
James Allan Christians, who is 65, is wanted for second-degree murder, aggravated assault and possession of a weapon.
Police say he may be driving a 2013 grey GMC pickup truck with Alberta licence plate JRA305.
The victim has been identified as 55-year-old Carmel Leah Christians.
Police say they had dealt with the couple before and a protection order was in place.