Iger had served on the board since 2011.
"While we will greatly miss his contributions as a board member, we respect his decision and we have every expectation that our relationship with both Bob and Disney will continue far into the future," Apple said in a statement.
His departure comes as Apple prepares to go head-to-head with Disney in streaming video.
Apple's Apple TV+ service is set to launch on Nov. 1. Disney's streaming video service, Disney+, is set to launch on Nov. 12.
"It has been an extraordinary privilege to have served on the Apple board for eight years, and I have the utmost respect for Tim Cook, his team at Apple, and for my fellow board members," Iger said in a statement. "Apple is one of the world's most admired companies, known for the quality and integrity of its products and its people, and I am forever grateful to have served as a member of the company's board."
Apple shares were down 0.07% in after-hours trade to $218.60. Disney shares also were little changed in late trade, edging up 0.08% to $138.13.