The 24-year-old, who has featured in all three of the Toffees' Premier League games so far this season, was forced off 20 minutes into his side's game against West Brom at the Hawthorns.
David Moyes believes the Republic of Ireland international could be back sooner than first anticipated because of the international break, which he believe has greatly benefitted the former Manchester United midfielder.
He told reporters: "Darron's got a thigh strain and will probably be out for four to five weeks now.
"He's had two weeks now so hopefully we are a couple of weeks down the line already because of the international break - so he may have only a couple of weeks to miss.
Gibson has enjoyed a good start to the season helping the Toffees pick up six points from their three games including an opening day win over Manchester United.
Moyes feels it's disappointing to lose a player who has been so influential for his side so far this campaign, as he's set to miss their games against Newcastle, Swansea and Leeds in the League Cup.
"It is a concern for me because Darron has been very consistent and he's been very good," added Moyes. "It's a blow and it leaves us a bit short in that area but we'll have to find ways of getting around it."