Barkley sustained the injury in his club's 4-0 FA Cup win over QPR on January 4 and is almost certain to miss the Merseyside derby at Liverpool at the end of the month.
After the midfielder sat out Saturday's 2-0 win at home to Norwich City, Everton manager Roberto Martinez revealed fears that he could be without Barkley for a prolonged period.
He said: "It looks like he's going to be out for a while.
"It could be (broken) and that's what we're worried about. It's a very similar incident to the one Leighton Baines had.
"Some can go a couple of weeks and others a bit longer like Leighton. Because it was a bad one it took six weeks."
Baines missed six games after picking up the same injury in the first Merseyside derby of the season at Goodison Park in November.
