McCarthy has made a big impact since his summer arrival from Wigan Athletic.
Asked whether the midfielder has the credentials to follow in the footsteps of past midfield Club captains, Martinez declared: "Yes, he has that. He's a real example.
"When you're talking about players who you want to set an example to the youngsters, he's clearly that.
"To be able to reach that landmark [250 appearances] at that age shows you that he's never changed, he just embraces challenges.
"He wants to get in positions where he can help the team and he's such a humble footballer and example of how a modern footballer should behave.
"Looking at the way he's been enjoying his football at Everton, it's been a real joy for everyone and he deserves that milestone and deserves to be an example."
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