The students, who were spectators at Christchurch Boys' High School's 27-28 loss to Christ's College on Saturday, were involved in "a bit of push and shove" between opposing supporters.
Stuff reported that students from both schools had met on the field after the final whistle, where some collar grabbing and shoving ensued, along with an exchange of words.
Meanwhile, Christ's College executive principal Garth Wynne described the incident as "scuffles" and had not received any formal complaints. No Christ's College students have therefore faced disciplinary action.
A string of arrests in 2009 then saw Christchurch Boys' High School endorse a Christ's College initiative to eliminate all alcohol from the event.
The two schools have faced off 136 times since 1892. Christchurch Boys' High School has won 84, whilst College has won 43. There have been nine draws.