Gilligan, 55, was coming back from a business trip. The plane made an emergency landing in the U.S., an American Express spokeswoman said. She declined to say where Gilligan had been.
"This is deeply painful and frankly unimaginable for all of us who had the great fortune to work with Ed," said American Express CEO Ken Chenault, in a letter to employees Friday.
Gilligan began working at the New York credit card issuer and global payments company 35 years ago as an intern. He was named president of the company in 2013 and reported to Chenault.
American Express said he is survived by his wife and four children.
In his time at the company, Gilligan worked on just about every area of American Express' business, including commercial card, small business, merchant services, travel and, most recently, digital partnerships and payments.
As a result, Gilligan was viewed as a potential candidate to eventually succeed Chenault, said Jim Shanahan, financial services analyst at Edward Jones.
"In my mind, he would have probably been one of a few people on a very short list, at least of internal candidates, to replace him at some point," Shanahan said. He noted, however, that he doesn't believe Chenault, 63, is likely to retire any time soon.
American Express has a "very deep management team," and it's possible someone else could be promoted to a more senior role and groomed for leadership of the company, Shanahan added.
Gilligan's passing comes at a challenging time for American Express.
Earlier this year, the company lost its exclusive relationship with Costco and lost a U.S. antitrust suit. A stronger U.S. dollar also dampened its revenue in the first quarter.
At the same time, the company has benefited from growing spending by cardholders.
In April, the company announced it would increase the annual fee on some of its popular charge cards, while also noting it would be beefing up some of those cards' benefits as well.
The New York-based company's shares are down 14 per cent this year.