Videos of the brawl, which happened in front of a child sitting nearby, started to appear on Twitter around 8:30 p.m.
In one of the videos, a Dodgers fan wearing a Mookie Betts jersey is seen repeatedly punching another man, presumably an Astros fan.
Another angle shows a woman in a white Astros jersey tending to the man who was beaten and bloodied.
During the brawl, a little girl is seen crying until someone in the row in front of her picks her up.
Dodgers' Joe Kelly suspended 8 games for throwing at Astros batters
KTRK-TV reached out to the Houston Police Department on Wednesday night as the videos started to circulate on social media.
The department said that it had not been called to respond to any incidents inside the ballpark, but any officers there were likely off-duty, working second jobs.
According to Dodgers fan @Helennnnaaaa_, who was at the game and captured video of the incident, every time the Dodgers fan cheered for L.A., the Astros fan would comment. She claims that the Dodgers fan grew tired of the remarks, but it was allegedly the Astros fan who threw the first punch.
Twitter user @Helennnnaaaa_ says both men were arrested.
The Dodgers and Astros have been far from friendly after the sign-stealing scandal involving Houston that rocked Major League Baseball in 2019.
Dodgers pitcher Trevor Bauer has been among the most vocal critics. He started Tuesday night for Los Angeles, who ended up falling to Houston, 5-2.
Astros shortstop Carlos Correa denied that Houston's win meant more because it came against the Dodgers and Bauer.
"A lot of people have said a lot, and that don't mean that we go out there every single day and try to win because of what they said," he said. "It don't mean much to us. We just go out there and try to win games."
The Astros salvaged a split of the two-game set in a rematch of the 2017 World Series -- a title Houston won over Los Angeles that became tainted when it was revealed the Astros illicitly stole signs en route to the championship.
The Astros won't face the Dodgers again until August, and next time, it'll be in Los Angeles.
The Associated Press contributed to this report.