"At this point we aren't concerned this injury will jeopardize his season," McDermott said.
McDermott, who did not provide a timetable for Jones' return, said it was "best for us to get this done now."
Jones is expected to start opposite Kelvin Benjamin this season.
It has been an eventful offseason for Jones. In March, he was arrested in Los Angeles on suspicion of felony vandalism after an incident at an apartment building. Jones was found "breaking glass doors and windows," police said at the time of his arrest. Video of the incident showed him naked in a hallway, arguing with his brother, Cayleb Jones, who is a receiver with the Minnesota Vikings. Prosecutors declined to pursue charges, citing insufficient evidence.
Jones, 23, had 27 catches for 316 yards and two touchdowns last season.