The shooting caused an outcry in Israel and sparked calls for the military to re-evaluate its rules of engagement and the way it deals with unarmed protesters.
During a demonstration 10 days ago, troops fired at a group of peace protesters who tried to cut through a fenced portion of the barrier, moderately wounding an Israeli demonstrator in his legs and lightly injuring an American protestor.
Israel says the barrier - made up of concrete walls, razor wire, fences and trenches - is meant to keep resistance fighters out.
Palestinians condemn the barrier, which dips deep into the West Bank in some areas, as a land grab.
While the incident appears to be the first time that Israeli troops had opened fire on Jewish protesters, critics say the army regularly uses live ammunition to disperse Palestinian protesters.
One of the soldiers responsible later said he would never have opened fire if he knew the protestors were Jews.
In a statement released on Tuesday, the army said the incident and its results were "serious", but no disciplinary steps would be taken against the soldiers who opened fire.
"Given all the factors involved, including the fact the soldiers felt they were under a real threat, the lack of accessible riot control gear and the rules of engagement the force was operating under, there was no deviation from the normal rules of engagement," the statement said.
However, the army said it would re-evaluate the rules of engagement for dealing with protesters near the barrier, in particular rules for opening fire with live ammunition.