Murray, who has shown no signs of discomfort on the field and managed to play 76 minutes during last weekend's loss to the Brisbane Broncos, will spend three to four weeks on the sideline.
The heart and soul of South Sydney, Murray was an omission from the team list to play the New Zealand Warriors during magic round in Round 10 and will now likely miss Round 11 and 12 as well before a Round 13 bye should allow him to return in Round 14.
Club physio Eddie Farah confirmed it was discomfort experienced in the shoulder over the last couple of weeks when speaking to club media.
"Cameron Murray had a shoulder reconstruction at the completion of last season," Farah said.
"He spent the summer in rehab strengthening the shoulder and returned to play this year without any problems.
"Unfortunately over the last couple of weeks he has developed some discomfort in the shoulder, so we sent him off for scans and he has seen a specialist this week.
"We have decided that the best management for him will be to have a minor shoulder procedure, and we expect him back playing in three to four weeks."
Jai Arrow has been shifted to lock to cover for the loss of Murray this weekend, and will likely remain there in the lead up to Murray's return to the side in a month's time.
South Sydney are also battling another potential out for this weekend, with Blake Taaffe reportedly ill and not training on Tuesday.