Investigators say they believe the man and woman were in the vehicle on Friday night when an argument broke out.
They say the woman tried to leave the vehicle but got tangled in the seatbelt and was dragged for a significant distance before the vehicle came to a stop.
Police allege she ran to a residence, and that when her husband caught up to her, there was a fight.
Police say they believe the man then left the area and went to a nearby hospital, which is when they say they were called.
A suspect, Gagandeep Sidhu, 30, of Calgary, has been charged with first-degree murder and will appear in court on Tuesday.
Police haven't released the woman's name or the cause of her death. An autopsy is scheduled for Monday.
Police said Saturday that the woman's family was not from Calgary and that they were having trouble contacting them to notify them about her death.
They asked anyone who may know how to reach the family to contact police.
Also on HuffPost