What exactly do you mean by literary criticism? Do you mean the close reading and analysis of a specific work or set of works, or do you mean theoretical treatises on literary aesthetics.
Pollock's Rasa Reader, that dragumannus pointed out is a good example of the latter but not so much the former. Anandavardhana' Dhvanyaloka (https://www.amazon.com/Dhvanyaloka-Anandavardhana-Abhinavagupta-Harvard-Oriental/dp/0674202783) is mostly the latter (a theoretical work) but he does a close reading of a variety of poems as part of the development of his theory, so there is some of the former there as well.
For purely stuff in the former category, I suppose the closest thing to this in premodern India is the commentarial tradition. But I am not sure if what they are doing is exactly the same as literary criticism. For an interesting look at the nature of commentary in Indian literature, I would recommend: Text to Tradition The Naisadhiyacarita and Literary Community in South Asia by Deven M. Patel.
For modern literary criticism regarding Sanskrit works: I recommend Alf Hiltebeitel's Rethinking the Mahabharata: A Reader's Guide to the Education of the Dharma King.
Also basically anything by David Shulman (though he tends to focus on South Indian regional languages more than Sanskrit). In particular, I would recommend his book, The Wisdom of Poets: Studies in Tamil, Telugu, and Sanskrit. Also his papers on Nala and the Uttararamacharita are quite good: On being human in the sanskrit epic: The riddle of Nala and Cruelty and Compassion in Bhavabhiti's Uttararamacharita.
Also, Emily T. Hudson's Disorienting Dharma: Ethics and the Aesthetics of Suffering in the Mahabharata is good.
Two of the most famous works on Indian aesthetics are the Abhinavabharati, which is a commentary on the Natya Shastra, an ancient work of dramatics and dance and aesthetics. I looked on amazon but didn't find a good translation. You can see the search results, but I haven't read these, so buy with caution, if you must.
The Dhyanavardhana with the commentary Locana is one of the definitive texts on poetics and aesthetics. It was translated by Daniel Ingalls, who is a famous scholar on Indian logic. The book however, is expensive, so check google books or a library first.
You can also check out the Wiki article for starters.
This talk by VS Ramachandran looks at Indian art through a neuroscientist's perspective, and is very interesting.
Good luck.