Three soldiers were filmed apparently aiming guns and firing at a poster of Jeremy Corbyn.
They can be seen shooting at the Labour leader, then smiling afterwards as they check how many shots breached their target.
Snapchat-style footage captioned, ‘Happy with that’, ends with a close up of Mr Corbyn’s face, now riddled with holes.
The corner of the video is marked 3 para (a shortened version of 3rd battalion parachute regiment).
An Army spokesperson said. ‘We are aware of a video circulating on social media, this behaviour is totally unacceptable and falls well below the high standards the Army expects.
‘A full investigation has been launched.’
The footage was captured in Kabul, Afghanistan.
It is understood it was a non-lethal hardened wax substance aimed and fired at the image instead of metal bullets, with the incident taking place in the past few days.
The video was also shared on Twitter by @StingRaeSpec, but has now been deleted. On his account he claims to be part of the Royal Navy, and tweets mainly about charity work helping veterans.
When we asked him to comment on the video, we were blocked from viewing his tweets.
It was also shared by an account in the name of ex-soldier Trevor Coult – who was awarded a Military Cross – last night.
It included a comment: ‘Not looking good for a Labour leader” alongside a crying laughing emoji. He later claimed the video was fake.
Twitter user Zach Martin responded: ‘Almost certain this is illegal but even if it isn’t against the law for uniformed military personnel to threaten death [on] a Member of Parliament, it’s undeniably f****** terrifying.
‘Gentle reminder that Jo Cox was murdered by a “British Patriot” less than three years ago.’
Sources earlier claimed the video could have been photoshopped, saying soldiers never fired at faces while training and only used ordinary targets.
A spokesman for the Parachute Regiment declined to comment.