Gibson was treated on the pitch for several minutes before being carried off with his right knee heavily bandaged and the midfielder will be assessed by Everton's medical staff on his return to Merseyside.
In a statement released via its Twitter account, the FAI said: "Darron Gibson has been assessed by our team doc and will return to his club for a scan with suspected knee ligament damage."
Gibson missed the start of the season with a knee problem and any extended absence would be a big blow to Martinez, whose side suffered only their first defeat of the season at Manchester City on 5 October.
The 25-year-old only recently returned to international football having made himself unavailable for Ireland after former boss Giovanni Trapattoni left him on the bench for the Republic's entire Euro 2012 finals campaign.
He played the full 90 minutes of the 3-0 defeat to Germany in Cologne on Friday night, but managed only 35 minutes at the Aviva Stadium on Tuesday before going down.