We present a neural Sanskrit Natural Language Processing (NLP) toolkit named SanskritShala (a school of Sanskrit) to facilitate computational linguistic analyses for several tasks such as word segmentation, morphological tagging, dependency parsing, and compound type identification. Our systems currently report state-of-the-art performance on available benchmark datasets for all tasks. SanskritShala is deployed as a web-based application, which allows a user to get real-time analysis for the given input. It is built with easy-to-use interactive data annotation features that allow annotators to correct the system predictions when it makes mistakes. We publicly release the source codes of the 4 modules included in the toolkit, 7 word embedding models that have been trained on publicly available Sanskrit corpora and multiple annotated datasets such as word similarity, relatedness, categorization, analogy prediction to assess intrinsic properties of word embeddings. So far as we know, this is the first neural-based Sanskrit NLP toolkit that has a web-based interface and a number of NLP modules. We are sure that the people who are willing to work with Sanskrit will find it useful for pedagogical and annotative purposes. SanskritShala is available at: https://cnerg.iitkgp.ac.in/sanskritshala. The demo video of our platform can be accessed at: https://youtu.be/x0X31Y9k0mw4.