Toronto police say they were called to the scene shortly after midnight after a report of a man armed with a hammer at the building.
The man was pronounced dead at the scene at 12:26 a.m., police said.
There was an interaction between Toronto police officers and the man, and one officer discharged his firearm, according to a press release from the SIU.
One subject officer and five witness officers will be part of the SIU investigation into the incident.
The SIU investigates reports involving police where there has been death, serious injury or allegations of sexual assault.