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 has been a huge asset for already for us this season in his role as captain and is totally respected by all the players. He's a true Scarlet and embodies all the values that we belong to as a rugby region and demonstrates that in his role as captain, leading by example.
"Despite being injured Mark will be back with the region for his recovery and during this time 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."
Jones will return to the region for his rehab and physio treatment in a fortnight following his post op recovery period.