The rights group names the Palestinian as 27-year-old Ashraf Abu Rahma.
He was hit in the foot by a rubber-coated steel bullet
Israeli media said the army arrested the soldier involved and that he told investigators his commanding officer, a lieutenant colonel, ordered him to fire.
Even though Abu Rahma was tied up and blindfolded, the officer said he told the soldier who shot the bullet only to shake his rifle to frighten the Palestinian.
According to reports, an Israeli military spokesman, said: "When the investigation is over and the results are in, steps will be taken."
Barak on Monday insisted the incident would be investigated.
"The Israeli military will investigate the incident, learn its lessons and hold those responsible to account," he said.
"Warriors do not behave like this."
The incident occurred three weeks ago in the Palestinian village of Nilin during protests against the construction of Israel's barrier in the occupied West Bank.
Michaela told Al Jazeera: "In my four years here, I haven’t seen anything this severe.
"However, the phenomenon of firing rubber coated steel bullets at protesters and the culture of whitewashing a community is very common amongst Israeli army officials."
Michaela said that high-ranking officials hardly try opening investigations that could potentially charge soldiers who commit such crimes, "and even when reports are made, the government rarely follows up on the charges to punish them through a military tribunal", she said.
According to Michaela, Israeli military regulations stipulate that rubber coated steel bullets are not permitted to be fired within a 40m radius, and officials are advised to aim for the legs only.
However, B'Tselem reported in a press release that the rifle, which appeared to have been modified to fire rubber-coated metal bullets, was aimed at least 1.5m away from his foot.
"I think the incident wouldn't have gained media attention had the video not been released and it forced him [Ehud Barak] to react. Otherwise, the incident would have been whitewashed and nobody would have known about it," Michaela said.