The video, shared on social media platform X, shows the career diplomat Jon Benjamin pointing the weapon at a person whose face has been blurred.
"In a context of daily killings in Mexico by drug dealers, he dares to joke," a post accompanying the video reads.
Earlier on Friday, the Financial Times reported that the ambassador had been removed from his post after the incident which it said occurred on an official trip to the states of Durango and Sinaloa in April.
Mexico has long reeled from violence linked to the country's warring drug cartels, with around 30,000 people murdered a year.
"We are aware of this incident and have taken appropriate action," said a spokesperson for Britain's Foreign, Commonwealth and Development Office.
Benjamin's LinkedIn page says his term as ambassador ended in May, and a biography posted on the government website for the United Kingdom notes he "was UK Ambassador to Mexico between 2021 and 2024."
Neither Benjamin nor the country's embassy in Mexico responded to a request for comment.
REUTERS