Jones underwent keyhole surgery yesterday to successfully repair torn cartilage in his right knee following an injury sustained in training with Wales last weekend.
Medics believe he will not be available for selection for a minimum of three months.
Head Coach Nigel Davies said: "It is very disappointing and unlucky for Mark at this particular time. It's one of the curses of modern day rugby unfortunately - it is a hugely physical sport and these boys train intensively on a daily basis.
"However, Mark is one of the most positive players I know in terms of coming back from injury. He deals with these set backs more positively than most people. He's been a huge asset for already for us this season in his role as captain, is totally respected by all the players and leads by example.
"He's a true Scarlet and embodies all the values that we belong to as a rugby region, respects our heritage and demonstrates his commitment to the Scarlets on and off the field.
"Mark will be back with us in a week or so for his physio treatment. Despite the injury, I know he will continue to play a key leadership and motivational role off the field with the players, as well as working closely with coaching staff and Scarlets management."