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.
"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."
"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.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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