Stones has risen to prominence this season and started Everton's last seven games in the absence of injured captain Phil Jagielka.
Martinez is delighted with the way the 19-year-old, who arrived at Goodison Park from Barnsley in January 2013, has quickly adapted to the Premier League.
However, the Everton manager has warned against expecting too much, too soon from the England Under-21 international.
"We need to allow him to develop," Martinez told Sky Sports. "He is going to have an England role (in the future).
"He is going to be an important player for English football, but we need to give him time and allow him to enjoy his football.
"His focus should be to keep his place and to make sure he doesn't drop his standard from now until the end of the season."
Martinez has not been shocked by the composure shown by Stones.
"His quality is not a surprise because I had the opportunity to follow his development when he was coming through at Barnsley and he has grown into a phenomenal footballer," the Spaniard added.
"As a centre-half he is as good as it gets, and he is only 19. He's a joy to have in the squad. He's so calm and composed on the ball and in the same way so aggressive in his defending.
"We are all excited about his development."
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