Northern Ireland stars Keith Gillespie and George McCartney were involved in a fight on an aeroplane before it flew the team from Iceland to London.
The incident came after a verbal exchange and punches were thrown before other players were forced to intervene.
IFA chief executive Howard Wells told BBC Radio 5live: "As I understand it there was an altercation, so we need to look into it and establish the facts.
"When we know what happened we'll take whatever action we deem appropriate."
The incident happened after Northern Ireland's qualification hopes were hit following a 2-1 defeat by Iceland on Wednesday.
"This doesn't help the image of the IFA and it doesn't help the image of the game"
Cabin crew reported the altercation to Northern Ireland manager Nigel Worthington before the flight took off.
Wells added: "The manager didn't see exactly what happened because I think it happened before he got on the plane, but we've spoken and we'll do what we need to do.
"I'm not totally in the dark as to what happened, but everyone has the right to state their case and express their opinion.
"I will be the first to admit this isn't helpful. It doesn't help the image of the IFA and it doesn't help the image of the game, but we are where we are and we have to deal with it."
Northern Ireland's hopes of making the Euro 2008 finals are fading after Gillespie's late own goal gave Iceland a 2-1 victory in Reykjavik.
The Sheffield United winger made his international debut in 1994 and scored twice in 78 appearances.
West Ham defender McCartney, who ended a 26-month exile when Worthington took over from Lawrie Sanchez, won his 25th cap in Wednesday night's Group F game.
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