The stock was down more than 2 percent in premarket trading.
Staggs will remain employed by Disney as a special adviser to Iger through the company's fiscal year. He will step down from his current role effective May 6. and will leave the company at the end of the fiscal year, Disney said Monday.
Disney said Staggs' departure will broaden the scope of its succession planning process to evaluate a "robust slate of candidates."
Sources told CNBC that Staggs is leaving the company because he didn't receive assurances from the board that he would succeed Iger.