Haydock Park officials are investigating after a mass brawl broke out among spectators.
About 50 people were involved in the fight before and during the eighth and final race of the day. A woman and toddler were caught up in the disturbance.
A spokesman said Haydock took a “zero tolerance position” on fighting and that those involved were “ejected”.
One man was arrested over a public order offence, Merseyside Police said.
Racing has been on high alert over on-track fighting after incidents at Goodwood, Ascot and Hexham in 2018.
The spokesman said Haydock is “continuing to work with the police on this matter”.