The 31-year-old, who played in the first two tests of the series win in South Africa that put Australia back on top of the world rankings, suffered the ligament injury playing Twenty20 cricket in India.
"It's a pretty significant injury," team physiotherapist Alex Kountouris told the Cricket Australia website.
"Shaun has had a short period of rest, but it's still a problem and we know that surgery takes a long time to recover.
"There's a three-to-four month recovery period and we've chosen to go ahead with that because it gives him time to play for Western Australia and prepare for the World Cup and the Ashes next year."
Lefthander Marsh, son of Australian opener Geoff, was a relative late-comer to test cricket and made his debut against Sri Lanka in Pallekele in 2011.
In nine tests since, he has scored 493 runs at an average of 32.86 with a high score of 148 against South Africa in the first test victory at Centurion in February.
A pair of ducks in the second test, however, saw him lose his place in the team for the decider in Cape Town to allow for the return of all rounder Shane Watson.
A more regular presence in the Australia one-day side with an average close to 40, Marsh is, if fit, likely to be included in the squad for the World Cup, which takes place next year in Australia and New Zealand.
(Reporting by Nick Mulvenney; Editing by John O'Brien)
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