"Investigators from the country's Ministry of Internal Affairs raided the data centre that was hosting the website's servers.
Torrents allow users to download music, video and other internet content by downloading small bits of files from others' computers at the same time.
The shutdown is the latest news in a campaign against file-sharing sites.
It follows the US's closure of Megaupload, and several European ISPs (internet service providers) being ordered to block access to The Pirate Bay.
Demonoid was listed alongside both of these sites in The Notorious Markets List - a document drawn up by the US government at the end of last year highlighting services that "merit further investigation for possible intellectual property rights infringements".
It noted that Demonoid "recently ranked among the top 600 websites in global traffic and the top 300 in US traffic"."