"Cricket Australia (CA) advises that Matthew Wade's scans have confirmed a sprained right ankle. Given the uncertainty of Wade's availability, Brad Haddin will fly from Australia to Mohali today to join the squad," CA said in a statement.
The visiting side trails 0-2 in the four-match series.
Wade had injured his ankle while playing basketball on Saturday.
Wade was in doubt before the second Test as well after he fractured his cheek bone during training but played through pain and scored a 62 in the first innings.
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He has been Australia's first-choice wicketkeeper since last April's tour of West Indies when Haddin left the series midway to be with his ailing daughter.
He has been in good form in the domestic circuit having scored 468 runs at an average of 52.00 with two centuries in the Sheffield Shield.