Barkley was one of the Premier League's breakthrough players last season but injured his knee on Friday, just a day ahead of Everton's opening game against newcomer Leicester.
Martinez said after the 2-2 draw that it was too early to "determine the extent" of the injury but that Barkley has a partial tear to his medial ligament.
Martinez says "that could be anything between seven weeks and I've seen injuries like that that take four or five months."
He added that "Barkley is a phenomenal footballer and we're going to miss him, there's no doubt about it. He was so sharp in preseason, I thought he came back with a different approach" after the World Cup.