The team is unsure as to how Jones sustained the injury, as he was able to complete team drills for the first time since an extended rest on Saturday.
Jones is expected to be out of action for the next five to six weeks, meaning that Mohamed Sanu is likely to take his place in the starting lineup. League star AJ Green will continue as the first-choice wideout.
Should the Bengals believe Jones can recover quickly, they may well still include him on the 53-man roster to start the season.
However, if he suffers a setback or doesn't make considerable progress, the team could place him on injured reserve and recall him after eight games.