Kohli could not field more than half the day after landing awkwardly on his right shoulder trying to save a boundary in the mid-wicket region in the post-lunch session.
He was treated with ice packs and later he was seen doing shadow practice inside the dressing room.
"There was a shock on his right shoulder, that's the current status. But the exact status of the injury will be known by tomorrow morning after we get the scan reports," India's fielding coach R Sridhar told reporters.
In case Kohli fails to take the field tomorrow, he will have to come lower down the order than his usual number four when India.
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Asked whether Virat would be able to bat, Sridhar said: "We will answer that when we get the correct status. Let's cross the bridge when it comes."
Such was the impact that he had difficulty in standing up and was seen grimacing in pain, clutching his right shoulder to be rushed out of the field immediately.
Sridhar said the ground was hard and sloping in nature.
A gentle flick off the pad from opener Matt Renshaw took the ball easily past the boundary as Australia scored their first runs in four in the first over of Ishant Sharma.
"We saw in the first boundary of the day when Renshaw got past Ashwin. He was trying to catch up but the ball beat him to the boundary line quite easily. That sums up the outfield situation.
"There are some slopes in the outfield and the ball runs hard. We can't really do much about it. We have to chase the ball. You have to try and dive and cut the ball if you're anywhere close to it.