Police say they made the discovery Thursday night after getting a call that a woman had been killed and her body taken across the city.
Officers received a separate call 20 minutes later from a woman who said she had been assaulted by the same man.
A third call from the public directed police to a bridge where a man in his late 20s was attempting to hang himself.
The man was rescued and taken into custody; he is being treated in hospital.
Police say early indications suggest the events were related to domestic troubles.
Investigators are focusing on an address in Calgary's southeast.
UPDATE: 4:00 p.m. -- Police in Calgary say the man tried to hang himself from a bridge after his girlfriend was killed. Police found the man hanging and rescued him, then they found the vehicle containing the body of a woman in her early 20s.