Executive vice president Stephen Jones said Wednesday the No. 4 overall pick will "miss some time" with a sore right hamstring, per the team's official website.
NFL Media Insider Ian Rapoport reported the injury is just a tweak and that Elliott's move to the sideline is precautionary.
Elliott's hamstring flared up Tuesday during practice and the running back was unable to finish the workout.
Jones said the team doesn't have a timetable for Elliott's return to the field, but the Cowboys will be very cautious with their first-round investment.
The Ohio State product is predicted to have a big role as a rookie. A dual-threat back, Elliott has the ability to carry the load on a three-down basis for a Cowboys offense that wants to get back to its ground-and-pound ways behind one of the best offensive lines in the NFL.
The Cowboys' backfield as a whole is banged up early in camp. Darren McFadden is on the active/non-football injury list after undergoing elbow surgery last month. Pass-catching back Lance Dunbar continues to rehab last year's knee injury. Free-agent pickup Alfred Morris is slated to get the majority of first-team carries until Elliott returns to practice.