1) Some might argue that the Harry Potter books are more popular than The Hobbit and The Lord of the Rings. But that argument is hardly persuasive. The Peter Jackson films were an international success, in India as much as everywhere else. In fact, preliminary plans have been drawn up to film a massive Bollywood trilogy of The Mahabharata, and producer Bobby Bedi has Peter Jackson’s film trilogy in mind as his model. He even wants to enlist the services of WETA on his own project. Of course, this news is three years old, so perhaps the film adaptation will never be made. But it proves that Tolkien has a popular place in India today. At least as popular as Harry Potter.
2) Since nearly everyone in India speaks English already, why bother translating Tolkien into Hindi (or Telugu or Tamil or Bengali or Punjabi or ...). But then why has Rowling been translated into Hindi? Sure, many Indians have read Tolkien in English, just as many have read Rowling in English. But if there’s demand for Harry Potter in Hindi, there ought to be at least the same demand for Tolkien. Certainly enough for a commercially viable translation. Not to mention: collectors who don’t even speak Hindi would line up to purchase a Tolkien translation, just as they’ve done for the Rowling.
3) the British and Hindi cultures are too incompatible. But considering their previous colonial relationship — i.e., the profound cultural influence England has had on India — it’s hard to see how this claim can hold water. Nevertheless, some have argued precisely this. In an essay with the evocative title, “Love Song of the Dark Lord: Some Musings on the Reception of Tolkien in an Indian Context” , Andreas Bigger suggests that “[i]f one tries to translate the LotR into an Indian language, one is faced with serious problems of intercultural understanding.” Fair enough, but apparently Bigger goes further, all but suggesting that a translation ought not to be attempted. I have not read his essay, but if I may lean on René van Rossenberg’s review of the Honegger collection ... Of Bigger’s paper, he writes that it
[...] is a bit of a curiosity. It discusses examples of problems a translator may encounter if The Lord of the Rings were ever translated into Sanskrit. All these problems stem from the cultural difference between Christians and Hindi. For instance, the term ‘Black Rider’ conveys to Europeans something foreboding, evil, but for an Indian reader the opposite is true. The author concludes that for a Hindu the book will always deal about [sic] foreigners, and that “the normally hidden racistic strand within Tolkien’s world at once becomes painfully visible. The Lord of the Rings becomes a book with a plain colonialist view that is trying to reestablish the ‘superiority’ of the Europeans over all other races of the world.” (p. 177) This is ridiculous. It is not the translator’s job to change the cultural identity of a work, and a Hindu reader can be expected to realise that the author has been working from a different cultural background. It is hard to imagine, and has not been proven by the author, that a careful translation of The Lord of the Rings into Hindi will become racist and neo-colonialist, for if a translation alters a book in such a way, then it is a poor translation. This paper is an example of oversensitive Western political correctness [...] 
I couldn’t have said this better myself.
Finally, 4) it’s just too difficult. That may be. If Rowling provides an enjoyable challenge with her anagrams and magical nomenclature, Tolkien’s work would be ten times more difficult and (I would think) frustrating to translate. The Lord of the Rings, with its tests and trials on every single page, must certainly be one of the most difficult challenges a translator can ever face. Add to this the fact that Tolkien’s admirers must be pickier (by several orders of magnitude) about the final product than Rowling’s — and perhaps this helps to explain the lack of a translation into even one of the languages of the Indian subcontinent.*
Nevertheless, it is a shame, because (pace Bigger) I think there is a strong synergy between Hindi literature and Tolkien’s world of Middle-earth. For just one example, “Chandrakanta, written by Devaki Nandan Khatri, was considered the first authentic work of prose in the Adhunik kaal (modern period). A story of magical characters, kings and kingdoms, it reminds one of The Lord of the Rings series [...].” Indeed, the magical quality of many Indian stories, with their sense of a mythology alive and well, would seem in some ways ideally prepared to embrace Tolkien almost as one of their own.
 Published in Honegger, Thomas, ed. Root and Branch: Approaches Towards Understanding Tolkien. Zurich and Berne: Walking Tree, 1999, pp. 165–179.
 Variations [a literature magazine of the university of Zürich] No. 4 (2000), pp. 177–180. Peter Lang Publishers.
* According to HarperCollins, either The Lord of the Rings or The Hobbit (they aren’t specific) has been translated into Marathi; however, I haven’t been able to find any tangible evidence of this. HarperCollins’s “to our knowledge” doesn’t inspire much confidence. They go on to say, “Please let us know if you find any more!” Please let the publisher know?! Err, shouldn’t they be the gatekeepers on this? ;)