The prognosis doesn't make positive reading for Jones, who will now miss at least four of Wales' five games in this year's Six Nations.
Jones will be unavailable for the tournament opener against England in Cardiff on February 4, as well as the home tie with Ireland and the trips to Edinburgh and Rome.
The 29-year-old could be back in contention ahead of the game against France in Paris on March 19 but his absence is expected to be strongly felt as Wales aim for a third Grand Slam in seven seasons.
Jones' injury leaves Wales severely depleted in the front row, with fellow Test Lion Gethin Jenkins having been ruled out through toe surgery.
Wales will also be without suspended scrum-half Richie Rees for the entire Six Nations, while centres Tom Shanklin, Andrew Bishop and Gavin Henson are all currently on the treatment table.