The firm has been monitoring the online game for some time and has also released its own authorised version of Scrabble on the networking site.
Hasbro said in its lawsuit that Scrabulous violates its copyright and trademarks. Separately, Hasbro asked Facebook to block the game.
Scrabulous has attracted some half-million daily users, despite efforts by Scrabble's owners to end it.
Video game maker Electronic Arts released an official version for American and Canadian Facebook users last week as part of a broader, year-old licensing deal with Hasbro, yet Facebook users have continued to spend countless hours on the unauthorised Scrabulous.
Now, Hasbro is trying to stop Scrabulous completely and collect unspecified damages.
Mark Blecher, general manager for digital media and gaming at Hasbro, said the firm waited until Thursday to file a lawsuit to ensure that Scrabble fans had a legal option first.
The lawsuit, filed in US District Court in New York, named as defendants Rajat and Jayant Agarwalla, the brothers in Calcutta who created the program, along with their Web design and technology company, RJ Softwares.
Mattel, owns Scrabble rights outside the US and Canada and did not join the lawsuit. It has a deal with RealNetworks to make a legal version available in other markets.