2:54 PM PT -- The LAFC and LA Galaxy have released a joint statement in the wake of the violent brawl ... saying they're disappointed in their fans' actions -- and are investigating it all.
"LA Galaxy and LAFC are reviewing fan incidents that took place during last night's match with local authorities," the teams said, adding a probe into a separate incident earlier this year is ongoing as well.
"These incidents violate the LA Galaxy, LAFC and Major League Soccer's Fan Code of Conduct and will not be tolerated. Fans in violation of this code will face disciplinary action including ejections and bans."
The teams continued, "We ask all fans of both Clubs to respect each other and find common ground as Angelinos and passionate fans of the sport. Let's build together."
2:15 PM PT -- Law enforcement sources tell TMZ Sports ... one person was arrested for battery for their alleged role in the melee.
The rest of the incident, sources say, is still under investigation.
Dozens of L.A. Galaxy and LAFC supporters were involved in a wild melee following the two teams' rivalry game Sunday ... and the entire, violent incident was caught on video.
A bystander captured the chaos at Dignity Health Sports Park in Los Angeles following the Galaxy's 1-1 draw with LAFC ... and you can see in the footage, multiple people threw and landed huge punches and kicks.
UNA BATALLA CAMPAL 🤦🏻♂️
La rivalidad entre los clubes angelinos, #LAGalaxy y #LAFC, se salió de control a la salida del estadio, y los puñetazos, patadas, insultos y agresiones se repartieron por todas partes, requiriendo de la intervención policial.