But they face competition from Matt Renshaw, who has been handed another opportunity despite misfiring in the domestic Sheffield Shield this season.
National selector Trevor Hohns said "there is no doubt the India series produced some disappointing results" and change was needed, after four Tests characterised by the failure of any Australian batsmen to score a century.
"Ultimately Aaron, Peter, Shaun and Mitch have not produced the performances expected of them with the bat at the Test level," he said.
"They have been given a good opportunity, but have not produced the scores we need."
He added, however, that the door was not closed and they must now prove themselves again in domestic cricket and the one-day series against India this month.
Pucovski was the shock call-up. The 20-year-old is one of the brightest batting talents in the country, scoring a double century for Victoria last year.
But he has only played eight first-class matches, and after that double ton took a break from cricket because of a mental health issue.
"We look forward to him joining the squad and congratulate him on his first national call-up."
Burns, who has played 14 Tests, has been knocking on the door this season with Queensland, while Renshaw has been unlucky not to get another call-up until now, since his last appearance at Johannesburg in April.
Australia squad: Joe Burns, Pat Cummins, Marcus Harris, Josh Hazlewood, Travis Head, Usman Khawaja, Marnus Labuschagne, Nathan Lyon, Tim Paine (capt), Will Pucovski, Matt Renshaw, Mitchell Starc, Peter Siddle
Cricket Australia XI: Joe Burns (capt), Kurtis Patterson, Scott Boland, Jake Doran, Jon Holland, Marnus Labuschagne, Michael Neser, Will Pucovski, Jason Sangha, Matt Renshaw, Chris Tremain.
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