Officers said they had also received reports of criminals trying to extort money from users of the site, which specialises in matchmaking married people who wish to be unfaithful.
They added that “spin-off” crimes were being attempted, such as online scams offering to help people have their information “deleted” from the web.
It was reported last week that 9.7 gigabytes of customer data and the details of about 33m members had been posted online by a hacking group calling itself The Impact Team, with website users identified through names, email address and other personal information.
Police confirmed on Monday that credit card details were included in the original dump of customer data but investigators believe this was limited to the last four digits of the main card number.
Toronto authorities added that Avid Life Media, which it said was co-operating fully with the investigation, was offering a $500,000 reward for any information that could help identify the perpetrators of the attack. Experts have said the company faces potential regulatory fines and legal action.
Avid Life Media did not immediately respond to requests for comment.
Toronto Police acting staff superintendent Bryce Evans addressed The Impact Team during a press conference, saying: “I want to make clear to you, your actions are illegal and will not be tolerated. This is your wake-up call.”
He said Avid Life Media staff became aware of the hack on July 12. They logged on to their computers and were confronted by a message from the hackers accompanied by the AC/DC song “Thunderstruck”.
The data dump occurred a month later, after The Impact Team threatened to expose Ashley Madison’s customers’ details unless the business was closed down “immediately and permanently”.
The company said this year it planned to launch an initial public offering in London, after previously having to reconsider plans to float in Canada and Asia, citing investors’ moral concerns about the business.
The group, which values itself at $1bn, owns other specialist dating sites such as Cougarlife.com and EstablishedMen.com. It had sales of $115m in 2014, representing a 45 per cent increase compared with the previous year, with 50 per cent of its business in the US.