The club said he had a "small fracture", but could not put an exact timescale on his recovery.
A statement said that, depending on how quickly the injury heals, the 20-year-old could be out for anything from three to six weeks.
Barkley suffered the injury during the Toffees' FA Cup third-round win over QPR last weekend, a match in which he also scored.
He missed the 2-0 Barclays Premier League victory over Norwich at Goodison Park.
England as well as Everton will be hoping the midfielder recovers as soon as possible.
He has made a huge impression this season, having been given regular first-team opportunities by Martinez, with his exciting performances and eye for goal earning him three England caps so far.
He is firmly in the reckoning for a place in Roy Hodgson's summer World Cup squad.
Should his recovery take longer than expected, he could miss England's friendly with Denmark at Wembley on March 5.
- Sports & Recreation
- Barclays Premier League