Footage posted on social media showed members of the Parachute Regiment in Afghanistan shooting at an image of Corbyn, Britain's main opposition leader. Corbyn, a veteran socialist, has often been critical of British military campaigns overseas.
Brig. Nick Perry, commander of 16 Air Assault Brigade, said "the video shows totally unacceptable behavior and a serious error of judgment that falls far below what we expect of soldiers in our brigade."
He said the video was being "fully investigated." "The army is and always will be a totally apolitical organization," he said. The brigade has 400 troops in Afghanistan as part of a NATO deployment to train Afghan forces.
Labour defense spokeswoman Nia Griffith tweeted that the video was "shocking and completely unacceptable." She said it was "right that the Army is carrying out a full investigation." Conservative lawmaker Tom Tugendhat, a former soldier, said the video was "disgraceful."
British politicians have reported increased threats and fears for their safety amid heightened tensions over Brexit. Last month, a man angry about Brexit was sentenced to 28 days in prison for hitting Corbyn with an egg.
In 2016, Labour lawmaker Jo Cox was murdered by a far-right extremist. A neo-Nazi was recently convicted of plotting to kill another Labour legislator.