Head Physio at the Scarlets Patrick Moran said: "Dafydd sprung his A/C joint on Saturday and the extent of the injury means he has had an operation to repair it. We will know more later in the week as to how the surgery went, but we can say that it's likely he will be out for three to four months.
"He will be back with us at the Scarlets in a couple of weeks after the op to begin his rehab work with us."
Scarlets Head Coach Nigel Davies said: "This is really disappointing for Daf, he has shown great form and commitment so far this season and thoroughly deserved his place with Wales for the autumn series.
"The key now is supporting him back to full fitness once he's recovered from the surgery and our medical team will be working closely with him at Parc y Scarlets.
"We are obviously frustrated with another injury to one of our senior internationals but we've shown in recent games that this squad has plenty of fresh, young Scarlet talent coming through and we have confidence in the ability and hunger being shown by these younger players.
"We all have to back these players and as they step-up and replace the big names like Mark Jones and Dafydd over the next three months and play their part in some crucial and challenging games."