On Facebook the game is known as Scrabulous and it allows users of the social networking site to play each other. More than half a million users do so daily with people able to play with friends and those they do not know.
The application was developed in Calcutta, India, by software developers Jayant and Rajat Agarwalla and launched at the end of June.
The pair had earlier developed their own online versions on the websites Bingobinge.com, and Scrabulous.com in 2006. Last year they put it on Facebook after an approach to Hasbro, which owns the rights in the US and Canada, received no response.
Initally the pair said that they were targeting just a few thousand users, but within weeks the Scrabulous application had 20,000 users and was growing fast and making the pair around £10,000 a month.
Now Hasbro has responded jointly with Mattel, which owns the rights to the board game internationally, and asked the applications be pulled.
In a statement, Mattel UK said: "Letters have been sent to Facebook in the US regarding the Scrabulous application. Mattel values its intellectual property and actively protects its brands and trademarks.
"As Mattel owns the rights to the Scrabble trademark outside the US and Canada, we are currently reviewing our position regarding other countries."
The addictive quality of the game is explained by one blogger:
"I have a confession. The reason why you’ve heard barely a peep from me isn't because I’ve been Tasered by zealous cops or abducted by aliens. Truth is, I've been fiendishly playing Scrabble Scrabulous on Facebook. I swear, it's like a Krispy Kreme donut with sprinkles of crack on top.
"After its integration with Facebook, Scrabulous is now delightful, convenient, and sticky. It's a great example of how to take a classic standalone product and turn it into an online service that connects emotionally and deeply with people.
"The proof is in the numbers. While the original Scrabulous.com hosts 20,000 active users, the Facebook port gets 260,000 players on weekdays and about 5m million hits a day."
It is this success that has finally prompted Hasbro to act.
Mike Lynd, intellectual property expert and Partner at Marks & Clerk, the patent and trade mark attorneys, said the games firms were more likely to opt for copyright rather than trade mark infringement as this was easier to prove.
"This is an unusual case as Scrabble's owners have the possibility of bringing both copyright and trade mark cases against Facebook. Mattel may prefer to focus on the copyright case as it would probably be easier to prove copyright infringement, than proving trade mark infringement. Although the Scrabulous name plays on the name of the board game, it may be difficult for Mattel to show that it is harmful to their Scrabble trade mark.
"However, brands and trade marks are given stronger, enhanced protection by the courts as they become famous. Mattel also owns trade mark registrations of the actual design, layout and colours of the Scrabble board itself. Scrabble is such a long-standing, historic brand that Mattel is likely to have national trade mark registrations in most if not all European countries as well as EU Community Trade Mark registrations."
This he added gives Scrabble's owners great freedom to manoeuvre, in terms of deciding exactly where to bring proceedings against Facebook, in other words to pick the forum likely to be most favourably disposed to trade mark owners.