De Jong, 29, played at the tournament with a heavy bandage on his knee. The Netherlands bowed out following a round-of-32 loss to Morocco on penalties.
"The injury was more serious than initially determined. Thankfully, at this stage there is no need for surgery, and I am now fully focused on my recovery," De Jong posted on Instagram on Thursday.
Barcelona start their bid for a third straight LaLiga title with a visit to Elche on August 23.