The sniper fired at him once, wounding him in the leg, after warnings shots and orders to disperse went unheeded, it said, adding that the video was taken by a soldier from another unit.
An Israeli airstrike Thursday killed a Hamas fighter and wounded another and troops later shot dead a man close to the border, Palestinian medical officials said, as tensions across the Gaza Strip border simmered. Among the casualties was celebrated photo journalist Yaser Murtaja, who was wearing his press vest when fatally shot.
The video emerged as attention is focused on Israel over the killing of 31 Palestinians in protests along the border with the Gaza Strip since March 30.
"Wow. They hit someone in the head", says an off-camera voice.
Breaking the Silence, an Israeli organisation of former soldiers, wrote on Twitter that the video "compels us to confront the reality of occupation - it is impossible to control millions of people against their will without morally degenerating".
Speaking at a ceremony concluding Holocaust Remembrance Day, Israeli Defense Minister Avigdor Lieberman advised Hamas to spend its resources on improving the lives of Gazans rather than on trying to destroy Israel.
As widespread protests along the Gaza border entered a second week last Friday, IDF spokesman Jonathan Conricus denied Israel is using excessive force against protesters in Gaza.
Yousef Munayyer, who directs the U.S. Campaign for Palestinian Rights, pointed out how extreme Israel's rules of engagement now are, in permitting lethal fire to be used against protesters who even approach its perimeter fence around Gaza.
The media is painting Israel as being overly aggressive and in some cases, flat out murderous, with the "protestors" who want to breach the border fence and return to lands they claim were once theirs. Politicians within the Israeli parliament spoke out against the scenes documented.
The Israeli military says it is conducting an internal investigation into soldiers' actions on the border.
The machine gun fire also set off sirens in southern Israel, the army said.
In a response to the video issued Tuesday afternoon, the IDF said in a statement that the video was filmed back on December 22 during what they termed "a violent riot".