Irish Football Association president Raymond Kennedy is looking into the incident between Keith Gillespie and George McCartney as a matter of urgency.
The Northern Ireland internationals were seen to trade punches as the Icelandair flight was about to depart Reykjavik to London Heathrow yesterday.
Other players quickly intervened to calm the situation and cabin crew staff reported the incident to Northern Ireland manager Nigel Worthington.
Kennedy told the Belfast Telegraph: “We will deal with this incident very quickly and I expect to speak to Nigel Worthington about it first thing.
“I realise I am in a new role now and I will not be shirking my responsibilities when something like this happens.
“It really was the final straw from what was a terrible trip with two defeats when we all expected so much more.
“You don’t expect something like this to happen at any level of football, never mind after an international.”
Kennedy added: “From time to time in football, players do fall out and things are said in the heat of the moment but we will have to find out if it has been more than that.
“We have to remember the players were cooped up in hotels for eight days and there was very little for them to do.
“Not for one second am I using that as an excuse, but it has to be taken into account.”
The dispute happened in the wake of Northern Ireland’s 2-1 defeat by Iceland with the hosts’ winner coming thanks to an own goal from Gillespie in the last minute.
Four days earlier the province had lost 1-0 to Latvia in Riga, also in a qualifier.