The Grand Slam centre opted to delay the operation in order to go on Wales' three-Test tour of Australia.
But he has had the minor procedure in Manchester on Tuesday and is set to be sidelined for five weeks.
"I've had this problem for a while and I will need surgery eventually. It's just a matter of timing that surgery," Davies said in May.
"I've been with the Wales and Scarlets physios and credit is due to both medical teams. It's something I've played with. I was first made aware of it when we played Australia in December."
Davies missed the end of the Scarlets RaboDirect PRO12 season as the region narrowly missed out on a place in the play-offs.
He returned to action with Wales Down Under and played in all three Test matches, and scored in the second, as the Six Nations kings crashed to an agonising 3-0 series defeat.
Davies is expected to make a full recovery and should be back in action before the beginning of the season.