The media giant beat analysts' expectations across nearly every division.
Disney's studio entertainment business saw revenues for the quarter fall 2 percent to $1.9 billion, while segment operating income rose 33 percent to $544 million. The company said this increase was due in part to the performance of "Frozen" merchandise.
The studio business did see lower theatrical distribution compared to the same time last year, and that owed to "Big Hero 6" paling compared to "Frozen" in the prior-year quarter.
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As for the movie business' next big venture, Iger said he has "had the benefit of seeing a fair amount of the footage" for the coming "Star Wars" title.
"I'm thrilled with the way it's shaping up, and I can't wait to show it to the world," he said.
Disney parks and resorts saw revenue jump 9 percent to $3.9 billion. Domestic operations had an increase in income, the company said, but there was a decrease on the international front.
The domestic successes include both higher volumes and increased guest spending at the parks and resorts, Disney said.
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The company has come under fire in the last month over a measles outbreak that officials traced back to its California theme park Disneyland. Park officials say anyone planning to visit the facility should be vaccinated beforehand.
Iger told CNBC that the parks business had not seen any impact from the outbreak. He said the current quarter is up from the prior year in both reservations and attendance.
"This was yet another incredibly strong quarter for our company, with diluted EPS up 23 percent driven by record revenue as well as significant growth in segment operating income," Iger said in the earnings announcement. "Our results once again reflect the strength of our brands and high-quality content and demonstrate that our proven franchise strategy creates long-term value across all of our businesses."
Disney's cable networks saw operating income decrease 2 percent because of higher costs and lower advertising revenue at ESPN, the company said.
The sports network saw programming and production cost increases because of a contractual rate increase for NFL programming and rights costs for the SEC Network. Advertising revenue at ESPN fell on lower ratings for some programs, Disney said.
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The company's stock has risen more than 9 percent in the last six months and is up 34 percent in the last year.
One contributing factor to its stock continuing rise is its motion picture division. Disney-owned Marvel Studios films have grossed nearly $3 billion worldwide, according to Box Office Mojo, a box-office-revenue tracking website. Marvel Studios will release "Avengers: Age of Ultron" on May 1. The company's animated hit "Frozen" has also grossed $1.2 billion worldwide, making it the fifth-highest grossing film of all time, the website said.
Disney announced Monday plans to push back the opening of its $5.5 billion Shanghai-based theme park to mid-2016. It had been slated to open by the end of this year, according to a Reuters report.
—Reuters contributed to this report