Prop Aaron Jarvis, lock Alun- Wyn Jones and flanker Dan Lydiate are almost certainly out of the opening clash with Ireland, while full-back Leigh Halfpenny, centre Jamie Roberts and lock Ian Evans are major doubts.
"He was coming through well in the last couple of games of the autumn, put in a strong performance against Australia and was making a real impact on our game against Exeter, so it's very difficult for him to take.
"But he will get plenty of support from here throughout the injury period.
"I am sure that a player of his experience, intelligence and ability will deal with this very well, and after a couple of weeks away to recover from the surgery he will be back and can be a very positive influence in our environment.
"We all want to show him as much support as we can. It's going to be tough to take, but the boys here are a very close-knit group so that will be a positive for him."
Priestland, who has won 22 Test caps, was a driving force behind Wales' outstanding push to reach the World Cup semi-finals in New Zealand last year.
He then featured prominently during last season's Grand Slam campaign and although his form dropped off, he remained a key member of the team, starting three of their four autumn Tests and going on as a substitute against Samoa.