He damaged the elbow during his time in India with Kings XI Punjab and has now been ruled out of cricket for between three and four months.
"Shaun had surgery on his left elbow to reconstruct the ligament and the surgeon has reported that everything went well," Cricket Australia (CA) physiotherapist Alex Kountouris said.
"He will now wear a brace for a period of time and will then commence rehabilitation on the joint, which is anticipated will take approximately three to four months to recover.
"We believe having the surgery now will still allow him time to recover and play for Western Australia and with the view of him being fit and available for Australian duty again mid-summer."
Marsh has played nine Tests, 45 One-Day Internationals and 13 Twenty20 Internationals for Australia and helped the Kings XI reach the final of this year's IPL, where they were beaten by the Kolkata Knight Riders.
A busy international summer for Australia begins when they tour Zimbabwe later this month, before playing Pakistan in the United Arab Emirates and then hosting South Africa, India and England in the build-up to the 2015 World Cup, which they co-host with New Zealand.
© Cricket World 2014