Davies has 38 caps for his country and started in the opening game for Wales against Ireland in the 2012 RBS 6 Nations but missed the rest of the tournament when he was banned for a tip tackle in the same game.
But, despite looking unavailable with Wales' final match in the tournament on March 16 against England, Davies hoped the second row would be back before the end of the season.
"Bradley had the surgery on Thursday which went well and the surgeons have done an excellent job," Davies told Wales Online. "By Monday we will know more about when he is back.
"It is going to be a few months but whether it is two or three we are not sure at the moment. But we are expecting to see him back before the end of the season."