The midfielder suffered the problem during last weekend's 2-1 win over Cardiff City at Goodison Park.
Despite initial fears over the severity of the injury, Martinez has revealed that Barry will train as normal with his teammates.
"We've been very fortunate," the Spaniard told the club's official website. "It was a strong knock but he was caught in a position that has allowed him to recover quickly.
"It was painful and he has got stud marks but it didn't affect any joints.
"The ankle and the knee are in perfect condition so luckily enough on this occasion Gareth is fine and today he will train as normal."
Everton are currently in sixth place in the Premier League table.