Authorised Facebook Scrabble was launched in North America last week
Hasbro, which owns the rights to Scrabble in North America, is suing the Calcutta-based founders of Scrabulous - a game available on Facebook.
Last week, an official version of Scrabble was released for Facebook users in Canada and the US.
Hasbro said that Scrabulous violates its copyright and trademarks and has separately asked Facebook to block it.
The suit was filed in the Southern District of New York against the brothers Rajat and Jayant Agarwalla.
Scrabulous has been one of the most popular activities on Facebook.
The social networking site has so far declined to take down the application, which could mean it too is vulnerable to copyright action.
"Over the past year, Facebook has tried to use its status as neutral platform provider to help the parties come to an amicable agreement," the company said in a statement.
"We're disappointed that Hasbro has sought to draw us into their dispute."
Rights to Scrabble outside the US are owned by Mattel, which is not involved in the legal action.
Mattel is planning its own Facebook Scrabble game.