Police said the breach was a matter of online security "worldwide", warned that the hack had already led to a series of "spin-off crimes and further victimisation" by people claiming to provide access to the leaked data.
Toronto Police has set up a bespoke Twitter account to handle the investigation, where anyone with leads or who thinks they are a victim can contact officers. More than 33 million people are thought to be affected.
Acting staff superintendent Bryce Evans said Toronto Police had "a good working relationship" on the matter with the FBI and Homeland Security in the US.
At a press conference in Toronto, officers said the company behind Ashley Madison was offering a $500,000 reward for anyone who could provide information "that leads to the identification, arrest and prosecution of the person or persons responsible for the leak of the Ashley Madison database".
"This hack is one of the largest data breaches in the world and is very unique on its own in that it exposed tens of millions of people's personal information," he said.
He also provided further details of what happened when employees of Avid Life Media, the company which owns Ashley Madison, logged in on 12 July, the day of the hack.
The best, worst, and most unusual dating sites
Show all 18
Mr Evans said employees were met by a message from the hackers, calling themselves The Impact Team, which was accompanied by music - AC/DC's "Thunderstruck".
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies