While there is currently no succession plan for Iger — who has less than two years left until his planned retirement — he said he will do what's best for the company. There had been speculation that Iger may extend his term until the board can find a successor, but the longtime CEO said nothing had been decided yet.
"While I'm confident that my successor is going to be chosen on a timely basis and chosen well, if it's in the best interest of the company for me to extend my term, I'm open to that. But there's nothing specific to announce at this point," Iger said.
Robert Luna, CEO of Surevest Wealth Management, told CNBC's "Closing Bell" that the after-hours move probably has more to do with its run than the specifics of the earnings release. Luna, a shareholder in Disney, said his firm had trimmed its position ahead of the earnings report following the runup.
The stock set a new 52-week intraday high of $111.99 on Feb. 1. The Dow component has surged about 16 percent in the past 12 months.
"It seems like, at least, the tide has stemmed quite a bit," said Luna.
Programming note: Disney Chairman and CEO Bob Iger is scheduled to appear exclusively on CNBC's "Fast Money" on Tuesday at 5:45 p.m., ET.
Correction: Operating income for Disney's media networks segment declined 4 percent from a year earlier. An earlier version misstated the percentage.
— CNBC's Julia Boorstin and Mack Hogan contributed to the report.