Pant was hit on the helmet by Australian pace man Pat Cummins while batting and did not return to keep wickets in India's crushing 10-wicket loss on Tuesday in Mumbai. KL Rahul had to take over.
"He is stable and all his scan reports are clear," the Board of Control for Cricket in India (BCCI) said in a statement.
The 22-yar-old has been discharged from hospital and sent to the National Cricket Academy in Bangalore for more tests, the statement added.
"His availability for the final ODI will be based on how he responds during the rehabilitation protocol."
Pant walked back to the pavilion after being dismissed by Pat Cummins following an attempted pull that got the top edge of his bat and onto the helmet, the ball then deflecting to point.
Pant made 28 in India's 255 before unbeaten centuries from David Warner and skipper Aaron Finch gave Australia an easy win in 37.4 overs to take a 1-0 lead in the three-match series.
The second match is on Friday in Rajkot with the series finale on Sunday in Bangalore.