The 21-year-old lefthander will miss the contest as he had fractured his hand while batting against Pakistan in the third one-day international on Sunday.
Playing only his second ODI, Connolly was forced to retire hurt in Perth after being struck on the hand by a Mohammad Hasnain delivery as Australia slumped to an eight-wicket loss to hand Pakistan a 2-1 series triumph, according to Reuters.
Scans later confirmed Connolly had fractured the fourth metacarpal on his left hand, CA said.
Josh Philippe will replace him in the squad for the Twenty20 series against Pakistan, which starts in Brisbane on Thursday with matches to follow in Sydney and Hobart.
CA have prioritised the preparation of their test players for the upcoming series against India over the two short-format series against Pakistan.
Josh Inglis, the back-up wicketkeeper in the longest format, is the only member of the squad for the first test against India in Perth who will feature in the T20 series.