Footage on social media shows fans pushing and fighting as they exit the home stadium of the Galaxy after Sunday's result. According to TMZ Sports, one person has been arrested for their involvement.
The fracas comes after reported incidents of fan violence in an Aug. 28 match between the two teams at Banc of California Stadium, home of LAFC.
The teams issued a joint statement that read: "The LA Galaxy and LAFC are committed to growing the sport and the culture of soccer in Los Angeles and beyond. We are proud to share one of the most exciting new rivalries in the world.
"We are also committed to providing a safe and enjoyable environment for our guests and their families at all events and games. Fan violence has no place at our matches. The type of conduct displayed at the Aug. 28 and Oct. 3 games does not belong in the stands or anywhere in our game.
"LA Galaxy and LAFC are reviewing fan incidents that took place during last night's match with local authorities, and a review of incidents that took place during the Aug. 28 match is ongoing. 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.
"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."
The rivalry, dubbed El Trafico, has become one of MLS' marquee matchups since LAFC joined the league in 2018 as an expansion side. The Galaxy, a founding member of the league, have won five MLS Cup titles while LAFC still seeks its first ever. The Galaxy lead the all-time series 5-3-5.