Captain Steve Smith was also sent home last week from Sri Lanka to rest before South Africa, where his side will play six one-day internationals, including one against Ireland, before returning home to face the Proteas in three tests in November.
"Both Mitchell and Josh have had big tours of Sri Lanka and have a heavy workload ahead of them with 10 tests to be played this summer," chairman of selectors Rod Marsh said in a statement.
"As such, it is important they are managed appropriately and we believe missing the tour of South Africa is the right time for them to take a break.
"This also provides a good opportunity for some of our up-and-coming fast bowlers to push for selection."
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Hazlewood will return to Australia from Sri Lanka immediately, Marsh said, and miss the final one-day match and the Twenty20 series.
Starc will remain with the team until the end of the tour.
Australia, who were hammered 3-0 in the test series in Sri Lanka, have wrapped up the one-day series with an unassailable 3-1 lead.
The final ODI is on Sunday in Kandy before two T20 matches.
(Reporting by Greg Stutchbury in Wellington; Editing by Ian Ransom)
