Barkley suffered medial ligament damage in training on Friday and missed out as Everton were held to a 2-2 draw at newly promoted Leicester City in Saturday's Premier League opener.
Martinez is unsure how long he will be without the England midfielder, who broke into the Everton first team last season, but is sure the injury will not knock his confidence.
|9/5||Everton are 9/5 with Paddy Power to defeat Arsenal at Goodison Park on Saturday evening|
"He won't be worried," the Spaniard is quoted as saying in the Liverpool Echo. "You worry if you've never had the opportunity to make a name for yourself in the first team and then you get an injury which becomes a big setback. Then you’re worrying: 'Will I get a chance to show what I can do?' That's not the case at all.
"Ross will take the time to refresh himself, work in certain aspects and he'll benefit from being away from the football pitches. He knows it's important everyone is eagerly awaiting him.
"Whatever the season is for him it won't be 10 months and he needs to make sure the time he has is full of quality and the right level of intensity.
"I've got no worries about finding him in a good frame of mind. He'll give us a boost when he comes back. We won't push him too early but we’ll be looking forward to when he can come back and lift us."
Everton face Arsenal at Goodison Park in the Premier League on Saturday.