The 19-year-old was taken to hospital for scans after he rolled his left ankle when taking a catch on the deep mid-wicket boundary and tumbled over the rope during the third day of the warm-up contest against a Cricket Australia XI.
Shaw was chaired off the field by India physiotherapist Patrick Farhart and a support staff member into the away team dressing room at the Sydney Cricket Ground (SCG).
"Shaw underwent scans this morning and the reports revealed a lateral ligament injury," BCCI said in a statement. "Shaw will be unavailable for the first test against Australia in Adelaide.
"He will undergo an intensive rehabilitation program to hasten the recovery and be available for selection at the earliest."
It was a massive blow for India with the promising teenager an almost certain starter in the four-match series after a spectacular debut against West Indies last month.
India's other opening batsman Lokesh Rahul has struggled for runs and the third option, Murali Vijay, is on the comeback trail after he was dropped following a poor tour of England earlier this year.
Shaw scored an attacking 134 on his debut against West Indies and followed up with a 70 and unbeaten 33 in the second test against the Caribbean side.
He was also impressive on Thursday with a sparkling 66, hitting 11 boundaries in his 69-ball knock.
India would hope to have him back in the starting lineup for the second test at Perth, starting on Dec. 14.
The touring side's bowlers also had a gloomy day on the field against the representative team, who reached 356 for six at stumps replying to India's 358.
The local side got off to a rollicking start to reach 114 without loss through an opening stand between D'Arcy Short and Max Bryant.
Off-spinner Ravichandran Ashwin broke the partnership by dismissing Bryant for 62, while Australia international Short fell to fast bowler Mohammed Shami after a knock of 74.
Shami took 3-67 to put India in a position of strength by reducing their opponents to 234-6 at one stage but they recovered through an unbroken seventh wicket stand of 122 for the seventh between Harry Nielsen (56) and Aaron Hardie (69).
(Reporting by Ian Ransom and Sudipto Ganguly; Editing by John O'Brien)
