One man was arrested on suspicion of affray and possession of a controlled drug but nobody has been charged, Merseyside Police said on Sunday.
Haydock officials ejected the perpetrators, and a spokesperson for the course said on Sunday: “We are extremely disappointed by the incident, which is completely out of character with a jumps fixture in February.
“Our security teams were on hand to bring this under control and eject those involved, and we had ample security to do so.
“We involved the police who we are continuing to work with on this matter and those involved will be banned from HaydockPark and all other venues in our group.
“We take a zero-tolerance approach because there can be no place for this type of behaviour in British horse racing.”
A statement from the British Horseracing Authority read: “Haydock Park has stated they will take a zero-tolerance response to this issue.
“We will support the racecourse and the RCA in taking the appropriate action regarding crowd security.”
The issue of violence on racecourses captured the headlines last spring when fights took place at Goodwood and Ascot on successive weekends, with tracks subsequently implementing more stringent security measures.