The unnamed soldier was working at a checkpoint near the U.S. Embassy in Cairo on Feb. 3 when he shot Omar Salah, who was selling sweet potatoes on a street, the Egyptian news organization Ahram Online reported Friday.
It was unclear what prompted the attack on the boy.
An investigation by the "military prosecution" is ongoing, a military source told Ahram.
Thursday military spokesman Ahmed Ali issued a formal apology for the killing, stressing Egypt's armed forces are committed to following correct legal procedures.
Human rights activists called for a symbolic funeral Friday for Salah at Cairo's Tahrir Square.