The 34-year-old will sit out a second-straight match as he recovers from a groin injury suffered in last month's ODI series against India.
Warner missed Australia's eight-wicket win over the tourists in the series opener last week after sustaining the injury during the recent one-day series between the sides.
"Cricket Australia's bio-security protocols do not allow them to re-join the squad in time for the Boxing Day Test", Cricket Australia said in a statement.
The MCG, which hosts the traditional Boxing Day Test, is in line to host back-to-back Tests with Cricket Australia set to make a call on the Sydney Test on Wednesday.
India left the Adelaide Oval reeling after posting their lowest total in Test history - an astonishing 36 after holding a 53-run first innings lead.
The players will not be replaced in the squad for the Melbourne Test, making it likely that Australia will stick with the makeshift opening partnership of Joe Burns and Matthew Wade.
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"I don't think it will be that hard".
Australia off-spinner Nathan Lyon, however, believes that despite Kohli's absence, India will fare better as they have many world class players.
On Wednesday, the official handle of the Board of Control for Cricket in India (BCCI) tweeted images of the team practising at the Melbourne Cricket Ground. I have watched him a lot especially when I have gone over to tour India and the subcontinent to try and learn from him. You still have the likes of Rahul and Agarwal as well who have been exceptional so I think there are enough guys in the Indian squad who can fill Virat's shoes, obviously, Virat is a world-class player.
"It is one of the days where nothing went right for them and everything went right for us.We are expecting them to come out firing and not have any scars from the other day. I'll hopefully learn something from that, move forward and play a little bit better in the next game", he further explained. However, Gambhir said that it is worth remebering that India had actually taken a first innings lead and they also have a bowling unit that can potentially bowl out the home team twice.
"To be honest, it has been an adaptable year for everyone, it is out of our hands, I am just hoping that everyone is staying safe in Sydney during this festive period, I know Cricket Australia is doing everything in their power", he added.
"The other day (in Adelaide) we also saw some pretty incredible fast bowling".