The San Diego Chargers are investigating a video that seems to show a stadium security guard masturbating on the sidelines ... just a few feet away from the team's cheerleaders, and we've learned the guard in question has already been fired.

The video showed up on Facebook Monday ... the day after the Chargers played the Raiders in San Diego. The clip shows a guy in a red jacket, repeatedly jerking his hand while in the pocket of his pants.

We checked, and the the jacket he's wearing does match up with other guards -- who work for Elite Security -- in Qualcomm Stadium.

The team hasn't identified the guy in the video, but issued a statement saying ... "We are aware of the disturbing actions of an Elite security staff member at Sunday’s game. We apologize to any fans who may have witnessed the incident."

An official from Elite security tells TMZ the company did its own investigation and has fired the guy.