The video shows four soldiers, allegedly from the 3rd Battalion Parachute Regiment, firing at a poster of the Labour leader.
Sources claim the soldiers involved are connected to the Merville Barracks at Colchester Garrison in Essex.
The shocking video was posted online with the caption ‘Happy with that’ before it was taken down for fear of the soldiers getting in trouble, sources said.
Today the MoD described the video as “totally unacceptable” and said a full investigation has been launched.
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 clip, originally posted to Snapchat, shows the four soldiers lining up, wearing khaki uniform and berets, shooting what looks like hand guns.
The camera turns to show air conditioning units, and then what looks like target practice ‘dummies’, before focusing on a photo of Corbyn’s face, covered in holes.
Some have claimed it was filmed in Afghanistan, while others claim it is in the UK.
Writing online, one person said: “Well done lads. Shame the moral police will be trying to take your beret for this!!”
Another added: “I’d use an ak47 take his f**king head off.”
Another wrote: “Wow some terrible weapon handling going on here.
“And do these boys don’t learn with all the snowflakes out there now they will all be investigated and sacked well done !!”
Shadow defence secretary Nia Griffith slammed the video on Twitter, describing it as “shocking and completely unacceptable”.
“Right that the Army is carrying out a full investigation,” she added.
The behaviour of soldiers who used an image of Labour leader Jeremy Corbyn as target practice is “alarming and unacceptable”, a party spokesman has said.
Defence Minister Tobias Ellwood tweeted: “If authentic this is unacceptable. Am looking into it.”