Explaining the operation, the 24-year-old said: "I needed to have a piece of bony growth removed. It's apparently a normal enough thing to happen to have this growth after the type of injury I had. It just needed removing. Everything went fine. I am back jogging so everything is going to plan.
"It is of course a bit frustrating but, I suppose it's part and parcel of the game and just a question of getting on with it. I am hoping to be back in full training by the time the Magners League kicks off."
Murphy will travel with the Munster squad to Chicago for Sunday week's Setanta Challenge Cup match against the US Eagles. Following further pre-season friendlies against Saracens (September 7) and Viadana (September 14) at Musgrave Park, Munster will begin their Magners League campaign in Cork with a game against Llanelli Scarlets on September 22.
Meanwhile, Munster have released former Wales international Chris Wyatt from his contract in order to allow him extend his career abroad.
Wyatt, 32, was due to end his association with Munster in December but sought an early release so he can take up an offer to join French club Bourgoin, who will clash with Ulster in the Heineken Cup's pool stages.
Commenting on Wyatt's move, Munster coach Declan Kidney said: "Obviously with five back-five players away with the Irish World Cup squad things could be tight but we believe we have the resources to allow us release Chris with immediate affect and we wish him well in the future."
Wyatt, who played twelve times for Munster last season, said: "I am grateful to Munster for their consideration. Myself and my family have enjoyed our time here in Munster where we have always been treated in a fair and friendly manner and made very welcome by the staff and fans alike."