Left-arm spinner Ashton Agar will join Australia's squad for the fourth and final Test against India in Sydney, captain Steven Smith said on Tuesday.
Cummins said the injury was "nothing major at all."
Zampa picked up his maiden five-wicket haul in one-day internationals to help the hosts defeat New Zealand
Australia have until Oct. 15 to make changes to their 15-man squad
Virat Kohli's woeful form continued as India 'A' were shot out for a paltry 135 by Australia 'A' in the second unofficial 'Test' in Chennai on Wednesday.
Australian teenage cricket star Ashton Agar's father has said that he knew the player could handle the fame after doing well for the national team and the family did not wonder if the sudden attention would go to his head.
New Zealand thrashed Australia by 53 runs in the first T20I to take a 1-0 lead in the five-match T20I series.
Glenn Maxwell and Steve Smith struck half-centuries as Australia beat Sri Lanka by two wickets in a thrilling finish to the rain-affected first One-Day International on Tuesday for a 1-0 lead in the five-match series.
Batting first after losing the toss, Sri Lanka started sluggishly and were reduced to 51-4 at the halfway mark of their innings after Richardson claimed two early wickets.
Leg-spinner Ryan Burl picked up 5 for 10 in just three overs on Saturday as Zimbabwe stunned Australia in the third One-Day International in Townsville, registering an exciting three-wicket victory and denying the hosts a series clean-sweep.
South Africa dug deep to deny Australia a 3-0 series sweep with a battling draw in the rain-disrupted third Test at the Sydney Cricket Ground on Sunday, finally finding some fight on the final day of a miserable tour.
Mitchell Swepson - in just his second ever T20I - took the big wicket of Virat Kohli
FIXTURES (Start at 14.40 local, 0910 IST, 0340 GMT)
Opener David Warner is still looking for his first Test hundred against Sri Lanka while Smith has managed only one century in his last 18 Tests.
Nathan Lyon, Agar, leg-spinner Swepson and young off-spinner Todd Murphy got the nod in the 18-member Australia squad with Zampa missing out.
KL Rahul dropped two places to be sixth while Virat Kohli remained static on 10th in the batters' list.
Australia eased to a six-wicket victory against Sri Lanka in the fourth Twenty20 international in Melbourne on Friday, barely needing to shift out of first gear as they heaped misery on the tourists who have yet to register a win in the five-game series.
India have already secured the Border-Gavaskar trophy and they will now be playing for a record-extending 16th straight series win at home
Speculation is rife over who would lead Australia should Finch fail to regain his fitness.
Steve Smith and David Warner's first batting partnership on home soil since their ball-tampering suspensions helped Australia to a series-sealing nine-wicket victory over Sri Lanka in Brisbane.
Australia's cricketers are getting help from sprint legend Usain Bolt to boost their running between the wickets for the upcoming Ashes Test series against England.
Steve Smith has branded India favourites to win the T20 World Cup after Virat Kohli's side outclassed Australia in a warm-up match on Wednesday.
Smith said the team trusted the security arrangements in place.
It's been more than a decade since India lost a Test series at home - they had lost to England 1-2 in 2012.
In his last five innings including the first practice match against Western Australia, Rohit has scored just 63 runs, including two ducks in the T20I series against South Africa.
In the T20 batting chart, India batsman KL Rahul lost a place to be at the third spot but skipper Virat Kohli retained his sixth position.
Captain Rohit Sharma's return will certainly give solidity to the top order in the second ODI against Australia.
Media reports have said pace spearhead Pat Cummins, opener David Warner and several others might miss the tours after returning home following the abrupt suspension of the Indian Premier League last month.
Ian Chappell feels that Ravichandran Ashwin will certainly be the biggest threat but the Australia batters need to be proactive against him.
'It was a surreal experience to represent the country. Thanks to everyone for your wishes. Looking forward for more challenges.'
The records set by Australia's Ashton Agar and Phil Hughes against England during the first Ashes Test at Trent Bridge, Nottingham on Thursday.
The Indian batters will have to put their best their foot forward against Australia in the series-deciding third ODI in Chennai on Tuesday.
IMAGES from the T20 World Cup Super 12 match played between Australia and Sri Lanka in Perth on Tuesday.
Cheteshwar Pujara is set to play his 100th Test match when India take on Australia for the 2nd Test of the Border-Gavaskar Trophy
The Australian team management chose Peter Handscomb ahead of Travis Head
While Agar is some way short of all-rounder status, Finch said the 26-year-old was working hard to get there.
Martin Guptill smashed a quickfire half-century as New Zealand cruised to a seven-wicket victory over Australia at Wellington Stadium on Sunday in the fifth Twenty20 international and secure a 3-2 series win.
Pace spearhead Jasprit Bumrah found his mojo as India got back to winning ways with a morale-lifting 13-run triumph over Australia in the third and final ODI in Canberra on Wednesday, salvaging some of the lost pride in a 1-2 series defeat.
Australia spinner Ashton Agar said he loved watching Axar Patel bowl in the third Test against England.