The unexpected move came little more than a year after Staggs had been promoted to chief operating officer, and about two years before Iger, Disney's chief executive and chairman, is due to retire.
A source with knowledge of the situation said Staggs, 55, had learned he was not guaranteed the CEO job and that the board was going to broaden its search for a new leader. Staggs and the company mutually decided he should step down, said the source, who requested anonymity because the reasons were not announced.
Disney, which operates television networks, theme parks and a movie studio, said in a statement that the board aimed to evaluate a "robust slate of candidates."
Iger has led Disney to record profits and executed successful acquisitions of Pixar, Marvel Entertainment and "Star Wars" producer Lucasfilm Ltd. But he recently acknowledged subscriber declines at Disney's sports network ESPN, raising concern among investors about how the channel would adapt to online streaming technology that is rapidly drawing viewers away from traditional TV.
"How do you transition to that five, 10, 15 years out?" said Diedrich, who recommends buying Disney shares. "There may be a need there for someone who has more experience with that consumer trend that is certainly here to stay."
Facebook Chief Operating Officer Sheryl Sandberg, who sits on the Disney board, has been seen as a potential CEO candidate. Facebook declined to comment.
Iger, 65, has insisted that he would retire from Disney in June 2018, though the board previously convinced him to extend his contract twice after he announced plans to leave.
Disney's shares fell 1.5 percent to $97.18 in after-hours trading on Monday.
Staggs will remain employed by Disney as a special adviser to Iger through the company's fiscal year, which goes through September, Disney said. He joined Disney in 1990 after working in investment banking at Morgan Stanley & Co.
CFO Jay Rasulo, who had been seen as Staggs' chief rival for the top position, said last June that he would step down.