Pant suffered a concussion after being hit on his helmet while batting and did not come out to keep wickets for Australia's chase, with KL Rahul donning the gloves for the hosts.
The BCCI said the 22-year-old Pant has been ruled out of the second ODI in Rajkot but would consider him for the third ODI in Bengaluru based on how he responds during his rehabilitation at the National Cricket Academy (NCA).
"He is stable and all his scan reports are clear," the BCCI said in a statement. "He has been discharged from the hospital and will head to NCA, Bengaluru to undergo his rehabilitation protocol."
Australia lead the three-match series 1-0 after winning the first ODI by 10 wickets. (Reporting by Rohith Nair in Bengaluru)