The talented English midfielder was subbed off at half-time of the Toffees' eventual 3-1 win over Fulham on Sunday with a calf problem.
When quizzed on the fitness of Barkley, Martinez told Sky Sports that the 20-year old would most likely shrug off the injury to get himself up for next Sunday's home clash with the Gunners who sit just four points ahead of the Toffees in fourth.
"He's good. You need to understand that Ross has got a great frame and sometimes when you get a knock on soft tissue in such a demanding week, you are going to suffer," he told Sky Sports.
"But in some ways he is a quick healer and we just hope he can be back for next week."
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