McGain has suffered a shoulder injury and returned to Australia on Friday, but the selection of his Victoria team-mate White as a replacement has to come as a surprise as he has not figured in a Test team since touring India in 2004.
Although White is an all-rounder who offers to replace the leg-spin that Australia have lost in McGain, his recent county role has been primarily as a batsman in short versions of the game.
However, White had the experience of playing against domestic teams in India earned him a place in the national team. Cameron was a part of visiting Australia A team that played in India recently.
"Bryce McGain's long-term unavailability due to a shoulder injury gives his fellow Victorian right-arm leg-spinner Cameron White an opportunity to join the Australian Test squad in India," said Andrew Hilditch, Cricket Australia chairman.
"We feel that Cameron's right-arm leg spin and experience in Indian conditions, where he has just returned after captaining the Australia A one-day team to a tournament victory, is the correct option and will provide a good balance to our slow bowling attack.
"Cameron's bowling has continued to improve over the past year at interstate level and his powerful batting adds extra depth and versatility to the squad."
White is due to join up with his team-mates in Bangalore on Monday, ahead of the first Test which starts on Thursday.