The army said in a statement on Sunday that judges found the captain, whose name it withheld, negligent "in opening fire which caused the death of Muhammad Ali Najib Said Ziyad, 16, from the village of Nazlat Ziyad" in the northern West Bank.
The conviction is a rare example of an Israeli soldier being successfully prosecuted despite 2849 Palestinians being killed since the start of the Intifada in September 2000.
During the incident, which took place on 4 October 2002, troops entered the village to look for a car bomb and a group of young Palestinians began throwing stones at their vehicle.
The captain then fired at the wall of a house near the crowd in order to disperse the gathering, but the bullet went in through a window and critically wounded the teenager, who later died from his injuries, it said.
The court ruled the fact that the accused opening fire was "clear negligence".
His use of live fire in the direction of the house was "unreasonable because it endangered the residents of the house and the gathering around it," the statement said.
The officer will be sentenced at a later date.