Smith captained Australia to an 82-run loss in the second one-day international Wednesday which tied the series 1-1.
"I hate missing cricket, but in the long run it will do me a world of good," said Smith who returns home with three one-day internationals and two Twenty20s still to be played.
"The schedule is very busy. I still want to take on the role in all three formats and do it to the best of my ability," he added.
Cricket Australia's chairman of selectors Rod Marsh said Smith needed time off.
"Steve has a large amount of cricket coming up in the next 12 months and we wanted to find a time for him to freshen up and these last five matches provide a good opportunity to do so," Marsh said in a statement.
"Regardless of the results of the first two matches our plan was always for Steve to take a break and refresh ahead of the ODI Series against South Africa next month.
"This is a great leadership opportunity for David, he has really embraced his role as vice-captain and we are confident he will do a great job in Steve's place."
Australia will also have to do without injured quick bowler Nathan Coulter-Nile for the rest of the tour.
"Nathan had been experiencing a gradual increase in lower back pain which is now preventing him from bowling at match intensity," said team physiotherapist David Beakley.
He will not be replaced in the one-day squad, with cover provided by Victorian pace-bowlers John Hastings and Scott Boland.
Australia's tour of South Africa begins September 27 with a one-day match against Ireland in Benoni after which they play five ODIs against the Proteas.