Israel's military said on Monday it was investigating last week's incident, which it said took place as young Palestinians were throwing stones at Israeli soldiers.
Osama Hajahjeh, 16, said he was trying to run from soldiers when he was shot on Thursday. He said the incident began after a funeral for a school teacher in his village of Tuqu, who had been hit by a car driven by an Israeli while walking at a busy intersection.
Hajahjeh said school was let out early for students to attend the funeral. After the burial, he said he was tackled by a soldier who jumped out of an olive grove and forced him to the ground. He said his hands were cuffed and his eyes covered with a cloth blindfold.
"They shot me the first time while I was trying to change my sitting position because they sat me on thorns," Hajahjeh told AFP news agency by phone from a hospital in the Palestinian town of Beit Jala, near Bethlehem.
According to the teenager, he was hit in the right thigh the first time.
"I started walking towards the villagers asking for help," he added, then the soldiers "shot me again and hit my left thigh."
He said that he had two operations and was in a stable condition.
Hajahjeh said he was uninvolved in stone-throwing and had been swept up in the soldiers' pursuit of others.
An image captured by a local photographer shows soldiers appearing to pursue a fleeing Hajahjeh with his eyes covered and hands tied behind his back.
The shooting set off a chaotic scene. Soldiers and Palestinians shouted at each other as the teen lay on the ground. One soldier took off the teen's belt and used it as a tourniquet to stop the bleeding.
Amateur video shows a masked soldier screaming and pointing a pistol at a group of anguished Palestinians as the teen lies on the ground. Later, a soldier and two Palestinian men then carry away the teen to medical care.