Soldiers from The Parachute Regiment firing at a picture of Jeremy Corbyn for target practice demonstrated “a serious error of judgment” according to their boss.
Brigadier Nick Perry who is Commander of 16 Air Assault Brigade said the Army was taking the matter “extremely seriously” and would fully investigate.
“The video shows totally unacceptable behaviour that falls far below the behaviour that we expect,” he said.
Brig Perry said there were currently 400 soldiers from his brigade working with Nato and Afghan partners in Afghanistan, where the footage is thought to have been filmed.
He said they were doing an “outstanding job in theatre” but this incident would be fully investigated.
Labour leader Mr Corbyn said he was “shocked” by the clip; his party said it had confidence in the investigation.
Mr Corbyn added: “I hope the Ministry of Defence will conduct an inquiry into it and find out what was going on and who did that.”
The short clip shows four paratroopers in uniform firing down the range before the camera pans to the target, a large bullet-ridden photo of the Corbyn, taken from the Labour party conference
A message reading “happy with that” can be seen on the footage, which has been viewed more than 10,000 times.
Corbyn is unpopular with the Forces and has previously accused the British Army of secretly directing the war in Yemen. He has also shown support for the victims of Bloody Sunday after soldiers from The Parachute Regiment opened fire in Northern Ireland in January 1972.
The Saville Inquiry into the killings concluded that all the victims were innocent and that the paratroopers lost their self-control and fired without discipline.