Various reports say the England midfielder received a knock on Friday when preparing for the Premier League opener at Leicester.
Barkley will undergo a scan in the next couple of days to assess the damage.
He was a key player for manager Roberto Martinez last season and earned a place at the World Cup on the back of his club performances.
However, the 20-year-old could be facing several weeks out and that would be a significant blow to Everton.
It has been reported that he could miss between six and eight weeks, meaning he could be out until the middle of October, missing Everton's opening seven fixtures of the season in the process.
Barkley made 34 league appearances in the league in a breakthrough 2013-14 season, scoring six goals, with his performances earning rave reviews.
An academy graduate, Barkley had been linked with a move away, with Manchester City and Chelsea rumoured to be interested in the youngster, but he outlined his commitment last month by signing a new four-year contract to remain at Goodison Park.
Friday evening's news also represented a potential blow for Barkley's short-term England chances.
Having made two substitute appearances and one start in Brazil over the summer, Barkley would have been looking to cement his place in Roy Hodgson's first team on a permanent basis.
But he may be forced to watch from the sidelines as the Three Lions begin their Euro 2016 qualifying campaign against Switzerland next month. If he is indeed ruled out for eight weeks, he would almost certainly miss the Group E clashes against San Marino and Estonia.
While he is raw and inconsistent, Barkley has all the attributes to be one of football's biggest stars. His technical and physical attributes are exceptional, and Roberto Martinez has clearly aided his development. There is a worry about his injury proneness, and setbacks like this do not help.
What it could mean is that Everton dip their toes into the transfer market again, although - having spent £28m on Romelu Lukaku - a loan move appears more likely.
Either way this is the last thing Martinez would have wanted on the eve of the opening weekend.
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