The adventurous left-hander, who is playing in the Indian Premier League, said on his website that he would not take part in the tri-series with South Africa and Zimbabwe.
Warner, 27, said his schedule, including last southern summer's Ashes series against England and the tour of South Africa, had taken its toll and he wanted to be at home ahead of the expected arrival of his first child in September.
Australia are set to play four one-dayers in the tournament in Harare, two against each African nation, as well as a potential final.
"That's because playing for Australia is what I've always wanted to do since I was a youngster and you never want to miss an opportunity.
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"After a long few months of non-stop cricket and, with a baby on the way, I need some time off."
Australian coach Darren Lehmann said family coming first was an important part of his team philosophy and he had approved of Warner's decision.
"We are 100 percent supportive of David choosing to stay home and await the birth of his first baby," Lehmann said.
"It is an important time in anyone's life and I am a firm believer that family comes first."
Warner has become an indispensable part of the Australian Test and ODI teams with eight Test centuries and two tons in the limited form of the game.