India are already missing the services of seasoned pacers Mohammed Shami and Ishant Sharma and the latest injury would add to the visiting team's woes in the four-match Test series.
Australia lead the points table with 76.6 % (Percentage of points or PCT) while India are second with 72.2% following their victory in the second Test against Australia at MCG.
Warner and Pucovski will rejoin the Australia squad in Melbourne on Thursday evening in preparation for the New Year's Test.
Both Smith and Labuschagne have not been among runs with Smith aggregating just 10 across four innings at an abysmal average of 3.33.
Johnny Mullagh Medal is a tribute to honour the captain of Australia's first sporting team to tour internationally.
The former India all-rounder declared Rahane's hundred as the turning point of the Boxing Day Test, calling his knock a display of 'unbelievable concentration'.
Tim Paine's side were already reeling after a comprehensive eight-wicket defeat in the Boxing Day Test that levelled the four-match series at 1-1.
Warner missed the first two Tests and the preceding three T20 Internationals as well as one ODI game against India due to a groin injury.
Smith feels that he has allowed Indian ace-spinner Ashwin to dictate terms to him in the ongoing Border-Gavaskar trophy.
India vs Australia 2020: We take a look at the five performances that helped India outclass top-ranked Australia in the 2nd Test