Reigning Allan Border Medallist Mitch Marsh will instead captain the side for five one-dayers against England after leading the team during the recent T20 World Cup.
Australia will also face Scotland and England in three T20s in September, before the 50-over matches start.
Cummins' absence is part of a "pre-planned, long-term load management strategy".
The star quick led Sunrisers Hyderabad to the Indian Premier League final in May, then went straight into playing in the T20 World Cup.
Cummins is currently turning out for Major League Cricket franchise San Francisco Unicorns in the United States.
"It's not so much resting, because Patty certainly won't be resting," chairman of selectors George Bailey said on Monday.
Australian selector George Bailey says resting Pat Cummins is part of a long-term strategy. (Darren England/AAP PHOTOS)
"It'll be a pretty heavy period for him in terms of he's got a couple of things he wants to work on physically.
"Obviously he's had a lot of cricket and this is an opportunity to get on top of those and really set himself up for the next period of time."
Star quick Mitchell Starc and allrounder Glenn Maxwell will sit out the T20s, but return for the ODIs.
It is the first tour following veteran opener David Warner's official international retirement, with young master blaster Jake Fraser-McGurk selected in both squads.
Veteran wicketkeeper Matthew Wade, who performed poorly during the T20 World Cup, has been left out in favour of Josh Inglis.
West Australian young gun Cooper Connolly has been included in the T20 squad - his first national selection.
West Australian allrounder Cooper Connolly has been selected in Australia's T20 squad. (Dan Himbrechts/AAP PHOTOS)
The 20-year-old allrounder has starred for Perth Scorchers in the Big Bash League, and he made a brilliant 90 when called up to play for WA in last season's Sheffield Shield final in place of an injured Cameron Bancroft.
"It's exciting, we haven't had that many bolters for a little while," Bailey said of Connolly.
"He's an exciting young talent.
"Hasn't played a great number of games of cricket yet, but we really like his versatility.
"His work through the middle order for the Scorchers has been really impressive.
"Handy left-arm spin as well, which is just a secondary skill, but it's something we're really keen to keep exploring."
AUSTRALIA T20 SQUAD: Mitch Marsh (capt), Xavier Bartlett, Cooper Connolly, Tim David, Nathan Ellis, Jake Fraser-McGurk, Cameron Green, Aaron Hardie, Josh Hazlewood, Travis Head, Josh Inglis, Spencer Johnson, Marcus Stoinis, Adam Zampa.
AUSTRALIA ODI SQUAD: Mitch Marsh (capt), Sean Abbott, Alex Carey, Nathan Ellis, Jake Fraser-McGurk, Cameron Green, Aaron Hardie, Josh Hazlewood, Travis Head, Josh Inglis, Marnus Labuschagne, Glenn Maxwell, Matthew Short, Steve Smith, Mitchell Starc, Adam Zampa.
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