"Initial tests performed in Melbourne have confirmed that Jackson Bird has a bone stress injury of the low back," team doctor Peter Brukner was quoted as saying by Cricinfo.
"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.
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.