Cummins skipped the ongoing Test tour of Sri Lanka for the birth of his second child but also has an ankle problem that flared up after the Test series win over India at the beginning of last month.
The development came ahead of the Champions Trophy, which is scheduled in Pakistan and the United Arab Emirates (UAE) from February 19.
“Patty is hugely unlikely, which is a bit of shame, and we’ve also got Josh Hazlewood, who is battling (to be fit) at the moment,” McDonald told radio station SEN.
“So that medical information will land over the next couple of days and we’ll be able to shore that up and let everyone know the direction.”
Cummins’ absence will leave the Australians searching for a captain for the one-day tournament.
Vice-captain Mitchell Marsh, who skippers Australia in Twenty20s, had already been ruled out of the eight-nation tournament because of a back injury.
Steve Smith has captained the Test side in Sri Lanka.
“Pat Cummins hasn’t been able to resume any type of bowling so he’s heavily unlikely, so that would mean that we do need a captain,” McDonald said.
“Steve Smith and Travis Head are the two that we’ve been having conversations with while we’ve been building out that Champions Trophy team along with Pat back home.
“They’ll be the two that we look at for that leadership post.”
Hazlewood was restricted to just two Tests against India in the recent series because of calf and side strains.