The Barcelona loanee was taken off on a stretcher after pulling up in the second half of Everton's 4-1 win over Fulham.
|4/6||Ross Barkley is 4/6 with BetVictor to make England's World Cup squad|
"Scans have now shown the extent of the soft tissue injury in his right hamstring, which is likely to keep him out for a few weeks," read the statement.
Martinez also reserved praise for another youngster - Ross Barkley - but is keen to ensure he does not get carried away ahead of a possible World Cup debut in Brazil next year.
"In football a week is an eternity, so for a few months it is going to be a waste of time thinking about what can happen in the future," said the Spaniard.
"You need to concentrate on the day-to-day work and that's where Ross is.
"But all he needs to do now is concentrate on his club role and make sure he is ready to help the team and enjoy his season and develop, and grow.
"Sometimes you get confused as a player [about] how you are going to affect what happens in the national team - but it is very easy. It is about what you do at club level."