The Mount San Antonio freshman offensive linesman was immediately ejected from the game after the incident during the middle of the third quarter at Ventura College.
He was later arrested on suspicion of battery and taken to Ventura County jail after the game's broadcast was reviewed, the Ventura County Star reports.
A brief clip of the incident circulated on social media, which shows the moment Schirmer allegedly struck the official.
A broadcaster is heard saying: 'Oh my God! The ref just got punched in the face by a player! What? I've never seen anything like that before in my life.'
Police say the official, whose name was not released, had broken up an argument between players and was struck while walking Schirmer back to his huddle.
'I was on the bench talking and I heard everyone going crazy so I jumped up and saw him on the ground,' Ventura College quarterback Jake Luton told the Star. There's no place for that in football,' he added.
Trainers from both Mount San Antonio and Ventura College immediately raced onto the field to tend to the injured official.
He was replaced and did not return to the game, which home team Ventura later won 34-29.
California Community College Athletic Association bylaws say striking an official is punishable by a five-year ban, according to the newspaper.