Jones said on his radio show that Murray was having surgery Monday.
Murray has 1,687 yards rushing and needs 87 yards to break all-time NFL rushing leader Emmitt Smith's franchise record of 1,773 yards.
Lance Dunbar and Joseph Randle split carries as Murray's backup in Sunday's 38-27 win over Philadelphia that gave Dallas the NFC East lead.
The Cowboys (10-4) need to win both remaining games to ensure the end of a four-year playoff drought. They finish the regular season at Washington.