Opening batsman David Warner tore an adductor muscle in the leadup to the four-Test series and was ruled out of the Adelaide opener as well as the ongoing 'Boxing Day' Test in Melbourne.
Pucovski was ruled out after suffering a concussion in the first warm-up game between Australia A and India A.
Steve Smith is not expected to return to training until at least Wednesday.
A fresh coronavirus outbreak in Adelaide forced Australian players, including captain Tim Paine, into self-isolation but the country's cricket board asserted that the first Test against India here from December 17 will go ahead as scheduled.
Images from Day 1 of the second Test between Australia and India, at the Melbourne Cricket Ground, on Saturday.
Australia coach Justin Langer believes managing the mental health of his bubble-weary players will be one of his key responsibilities during the upcoming home series against India.
The legendary batsman congratulated Siraj for his feat and showered praise on Shardul.
With Warner, who missed out a major chunk of the India assignment due to a groin injury, looking fit for the job, dropping Burns was an easy decision to make.
Travis Head returned from COVID-19 to smash a belligerent 101 and Cameron Green made 74 to revive Australia after a top-order collapse on the opening day of the day-night final Ashes Test against England on Friday.
Usman Khawaja scored his second century of the match to help Australia to 265 for six declared on the fourth day of the fourth Ashes Test on Saturday, handing England an unlikely victory target of 388.
Kuldeep Yadav, among all the players in this team, has more experience of playing with pink ball and the kind of revolution he produces, he could make it difficult for batsmen to spot the black seam of the pink kookaburra under lights.
Australia should stick with Joe Burns as David Warner's opening partner for next month's first Test against India
Having finally bowled India out for 336, Australia finished Day 3 on 21 for no loss, an overall lead of 54 runs in the final match of a see-saw series which remains level at 1-1.
Saini limped off the field due to groin pain and was taken for the scans.
'I tended to agree with the gamble in that I didn't see an obvious replacement with Pucovski out, I was hoping he'd be fit to play.'
Wriddhiman Saha, on nine, and Ravichandran Ashwin, who is 15 not out, will return on Friday hoping to continue India's march towards the 300-mark.
Smith was forced to skip Tuesday's training session but Paine said he thought his predecessor as captain would be ready to go
Usman Khawaja celebrated his recall to the Test arena after two years in the wilderness with a stylish 137 to drive Australia to a declaration on 416 for eight shortly before the close of play on the second day of the fourth Ashes Test on Thursday.
Gautam Gambhir feels Virat Kohli's team will keep facing the problem of imbalance till it finds a suitable replacement for a half-fit Hardik Pandya
England's batting once again disappointed against Australia on Day 2 of the third Test
India's captain Ajinkya Rahane on Monday said the racial abuse faced by his teammates Jasprit Bumrah and Mohammed Siraj during the third Test against Australia in Sydney is not at all acceptable and should not happen anywhere in the world.
Paine said Pucovski would open the batting if he was selected for the match
Matthew Wade said he would be happy to remain at the top of Australia's order for the rest of the series
Siraj was rewarded for his tough decision as he took two wickets on an emotional debut to help India bowl Australia out for 195
Wriddhiman Saha's superior glovework may be given preference over Rishabh Pant's blazing blade in India's opening day-night Test against Australia, starting at the Adelaide Oval from Thursday.
Since 2011, England have managed to eke out just a single draw in 13 Ashes Tests over three tours and their last two Tests in Sydney have resulted in humiliating defeats.
Usman Khawaja will replace Travis Head in Australia's middle order for this week's fourth Ashes Test against England in the only change to the side that wrapped up the series in Melbourne last week.
Hazlewood to miss out again as Australia announce unchanged playing XI for final Test
Australians survived a barrage of bouncers under lights from Indian pacers before the match ended in a draw at the Sydney Cricket Ground.
Australia spinner Nathan Lyon said there is no room for racial abuse in sport and hailed India pacer Mohammad Siraj for calling out racial abuse during the recently-concluded third Test in Sydney.
England face a rejuvenated Australian team who have turned day-night cricket into a competitive advantage, winning all eight of their Tests under lights dating back to the format's 2015 debut.
Former Australia batsman Neil Harvey, who made his Test debut at the age of 19 in Don Bradman's formidable 1948 side, has urged selectors to consider young talents Will Pucovski and Cameron Green for the upcoming series against India.
Images from Day 1 of the Day-Night Tour match played in Sydney on Friday.
Wade will instead head to New Zealand with Australia's Twenty20 squad for a five-match series starting on Feb. 22 in Christchurch.
Play was halted for a few minutes after India pacer Mohammed Siraj complained of racial abuse from a section of the crowd
Images from Day 2 of the Pink-ball first Test between Australia and India, in Adelaide, on Friday.
Bumrah removed Australia openers Joe Burns and Matthew Wade for eight runs apiece in quick succession before tea, however, and Ashwin (4-55) drove home the advantage after the break.
Shubman Gill said it can be 'quite intimidating' to play cricket in Australia but asserted that his team will not back down when faced with either sledging or short-pitched deliveries during the four-Test series, starting in Adelaide on December 17.
Virat Kohli's tourists are the second ranked ODI side in the world and will be looking to get into their groove in the three 50-over and three Twenty20 matches that precede the four-match Test series around the new year.
Skipper Ajinkya Rahane reveals India's game plan going into the final day of the third Test against Australia.