The attack was reported at about 9:45 a.m. at the park, located at the corner of Geneva Avenue and Moscow Street.
Investigators learned that the referee had called a foul against a player, who was so upset at the call that he "performed a martial arts kick" to the referee's face, police said.
The ref was knocked out for a few seconds, and the player fled before he could get back up. However, the player failed to pick up his ID card that he had left at the registration desk, and the card has now been booked into evidence, police said.
The referee was taken to San Francisco General Hospital but was not seriously injured, according to police.