It is alleged the team from St Aloysius College in Glasgow returned to their changing room, opened their windows and started sectarian chanting after a win over The Glasgow Academy.
The incident is understood to have happened at the Academy’s New Anniesland ground in the west end of the city.
Parents standing near to the changing rooms were said to have been shocked.
It was also claimed there was an altercation between the two coaches.
A spokesman for St Aloysius – which charges fees of more than £11,000 per year – said: “The head master has been made aware of an alleged incident which it is claimed took place at a rugby match against The Glasgow Academy on Saturday, September 8.
“However, initial accounts differ from those described.
“A senior member of staff was present at all times and the verbal exchange between the two coaches related to a decision made by the referee during the match.
“After being approached by a Glasgow Academy parent regarding possible behaviour in the changing rooms, a member of staff investigated immediately.
“St Aloysius’ College takes complaints like this very seriously and a full investigation is currently under way.
‘We do not condone this type of behaviour at any time.
“Anyone who is found to be acting in a way that does not uphold the high standards of conduct come to be expected of pupils at the College will be sanctioned appropriately, as per our disciplinary procedures.”
An Academy parent, who declined to be named, said: “I could only describe the noise coming from the St Aloysius changing room as bellowing.
“It seemed to be all about the IRA and other Irish-related things.
“Parents were clearly upset and it must have been very embarrassing for people who were there to support St Aloysius.”
St Aloysius College is located in the city centre, with former pupils including actors Tom Conti and Sanjeev Kohli.