Religion in India

The closest formal qualification currently available is either in Sanskrit or Indology.
There are a few institutes that I would personally recommend, based on my acquaintances with the alumni and campuses viz.
Maharaja Sayajirao University of Baroda, Vadodara, Gujarat
MSU, Baroda has a long and proud history in Indology and Sanskrit studies. The Oriental Institute has the unique honour of being home to the Critical Edition of the Ramayana.
But for M. A. and M. Phil courses you should look to these faculties
Department of Sanskrit, Pali and Prakrit, MSU - The focus of the courses here is language and literature
Baroda Sanskrit Mahavidyalaya - This is an institute for traditional Sanskrit studies - including the Yajurveda, Dharmashastras and Jyotisha
Sagar University, Sagar, Madhya Pradesh
Sanskrit Department, University of Madras, Chennai
Allahabad University, Allahabad
Aligarh Muslim University, Aligarh
Kashi Vidyapeeth, Varanasi
Bhandarkar Oriental Research Institute, Pune and the Oriental Institute, MSU, Baroda are research institutes, and don't offer courses of any kind.