The Republic of Ireland international missed Sunday's 2-1 home defeat by Chelsea because of the injury.
Boss David Moyes said: "I think he's going to be out for about four weeks."
Gibson, who suffered his current injury in training, only returned to action in November after two months out with a similar complaint.
He missed 10 Premier League matches as a result and a further absence is a significant blow to Everton as he has been one of their key players since arriving in January.







