"He will undergo further tests tomorrow (Thursday). He will not be re-joining the team in India."
Bird played in the first warm-up game of the tour against Board President's XI and bowled 10 economic overs giving away only 10 runs.
A likely recovery time will not be known until Bird has further tests but it is a worrying development for Australia in an Ashes year, given how well his accurate seam-bowling style could translate to English conditions.
The loss of Bird leaves Australia with a 16-man squad ahead of the second Test, which starts in Hyderabad on Saturday.
At this stage, the selectors have not decided on whether to send a replacement player to join the group, leaving Mitchell Johnson as the only extra fast bowler in the group besides those who played in the first Test.