The midfielder went down in the 37th minute of the Republic of Ireland's 3-1 FIFA World Cup qualifying victory over Kazakhstan on Tuesday - a game attended by Everton manager Roberto Martinez.
And interim Ireland boss Noel King has revealed the former Manchester United man may now be out for the remainder of the campaign.
"It’s awful. It might be a few months," King told Setanta Sports. "It won’t be easy (for him) to get back this season."
Martinez reportedly left his seat at the Aviva Stadium to join Gibson in the medical room, but the Spaniard will now be forced plan for life without him for the foreseeable future.
Gibson was playing just his second match in the Ireland shirt after returning from self-imposed exile following the departure of previous coach Giovanni Trapattoni.
The 25-year-old has made only one Premier League appearance for Everton this season, after a ligament injury picked up in pre-season ruled him out of his side's early fixtures.
