Bhuvneshwar has been struggling with an ankle problem in recent weeks and has not featured during the first three days in Adelaide, where India trail by 148 runs with five first-innings wickets in hand
He will head home for treatment with a view to returning for the remainder of the four-match series, as Kulkarni gets his chance.
"Dhawal Kulkarni will join the Indian team for the ongoing Test series against Australia as a replacement for Bhuvneshwar Kumar, who has an ankle injury and will return to India to undergo a rehabilitation program," read a BCCI statement.
"Bhuvneshwar Kumar will rejoin the Indian team for the Test series in Australia, as soon as he recovers and is declared fit."
Kulkarni has yet to make his Test bow for India, but has featured in four one-day internationals - three against Pakistan in India and once against England in Edgbaston.