Deputy President Cyril Ramaphosa will stand in for Zuma at the funeral on Saturday of Epainette Mbeki, mother of former president Thabo Mbeki, and at Youth Day celebrations on Monday.
Ramaphosa is already presiding over the first meeting of Zuma's new cabinet this week while the president is resting at home ahead of his scheduled address to parliament.
Zuma spent the weekend in hospital for tests after officials from his African National Congress asked him to take a break because "the punishing election programme was taking its toll".
His office said the president has two "major" routine medical examinations each year - in January and in June.
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"This time round, the doctors felt he needed to be hospitalised for a thorough check-up following a demanding schedule," said the presidency.
Earlier Bongi Ngema-Zuma, one of the president's four wives, told reporters that he was "doing very well" and "just needed time to rest".
The presidency said today Zuma had requested next week's state of the nation address to be brought forward from Thursday to Tuesday so he could attend the African Union summit in Equatorial Guinea.