Martinez was in his first year as a professional coach. He was in the dugout for Sunday's 3-2 win over the Pittsburgh Pirates, then met with Marlins officials and resigned.
"I want to apologize to the Marlins organization for my behavior," Martinez said. "I have made some comments to certain players at certain times that I thought was more constructive criticism. Obviously, they didn't feel that way, and it kind of backfired on me."
Martinez said he once touched a player in anger, grabbing rookie Derek Dietrich by the jersey in the batting cage early this season. Dietrich, recently demoted to Triple-A New Orleans, was among the players to complain about Martinez.
Martinez, 45, was a member of four World Series championship teams during his seven seasons as the New York Yankees' first baseman.
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Information from The Associated Press was used in this report.