Earlier reports indicated that Moore, who was carted off the field, broke his right fibula.
Moore, who will need surgery, will be out a minimum of six to eight weeks.
The injury occurred when a defender rolled up on Moore's leg after the quarterback threw a pass. Brandon George of the Dallas Morning News reported that left guard Jared Smith stepped on the Moore's ankle, causing the injury.
"It's regrettable, and we'll basically just take a look at it and address it there," Jones said. "I don't have any comments about what, if anything, we'll be doing there."
Moore, 27, was slated to be Tony Romo's backup this season, and his injury obviously creates a huge hole in the depth chart. The fifth-year pro threw for 779 yards with four touchdowns and six interceptions in his career, all last season in three games, including starts in the Cowboys' final two games of the season.
"Your heart hurts for him," Cowboys tight end Jason Witten said. "He just works really hard. ... He'll continue to fight. That's who he's been his whole life."
Third-string quarterback Dak Prescott, a rookie fourth-round draft pick out of Mississippi State, replaced Moore in team drills after the injury.