The club said he had a "small fracture", and he could be out for anything between three and six weeks.
Barkley suffered the injury during the FA Cup third-round win over QPR last weekend, a match in which he also scored.
It forced him to miss the 2-0 Premier League victory over Norwich at the weekend.
Barkley has made a massive impression this season and has forced his way into the England squad, winning three 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.
Everton left-back Baines spent a month out of action prior to Christmas after picking up a similar injury.