The Sports Torrent Network had offered links to European football matches, US National Hockey League games, Formula 1 races and sports-related documentaries, among other content.
Torrentfreak reported TSTN had about 20,000 members, making it "possibly the largest site of its type".
The news site added police had emailed the service a fortnight ago.
"Pipcu has the lawful right to pursue action against you and against the thesportstorrentnetwork.co.uk website in order to prevent, detect and disrupt criminal activity," read the warning from the City of London Police Intellectual Property Crime Unit.
The message added that the operators faced up to 10 years' imprisonment if found guilty of encouraging and assisting the public to share pirated material.Membership incentives
Like many other torrent trackers, TSTN did not host pirated media files itself but, rather, helped connect users wanting to share files over peer-to-peer networks.
Members had to tell the site's administrators the reason they wanted to join before being allowed access. They could, however, invite others if they had seeded enough content or made a big enough donation.TSTN members shared links to material including NHL hockey games
"Thanks for being around with us for the last few years. Best regards, TSTN crew."
The City of London Police launched Pipcu in September last year after securing £2.56m from the UK's Intellectual Property Office.
Its officers act on tip-offs from industry groups to identify UK suspects and seek out websites offering illegal goods and downloads.
It has previously closed several other smaller sports-related sites - including boxingguru.co.uk and nutjob.eu - and arrested a man accused of selling set-top boxes that allowed illegal access to Premier League Matches.
It has also created a database of "illegal" websites that it has shared with the advertising industry in a effort to cut off revenue to the offending sites' operators, but has not made the sites' names public.
Pipcu's own funds are due to run out next year, but the prime minister's Intellectual Property Adviser, Mike Weatherley MP, has urged David Cameron to fund the unit on a permanent basis.