He said the video was being "fully investigated."
"The army is and always will be a totally apolitical organisation," he said.
The brigade has 400 troops in Afghanistan as part of a Nato deployment to train Afghan forces.
Labour defence 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 MP 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 MP Jo Cox was murdered by a far-right extremist. A neo-Nazi was recently convicted of plotting to kill another Labour legislator.
- AP