Fisher died at his home in San Francisco after a long battle with cancer, the company said.
Starting with a single store in San Francisco, Fisher and his wife, Doris, built the Gap into a brand name recognized around the world. Gap jeans, khakis and T-shirts became the uniform for a generation of Americans and were at home even on the red carpet on Oscar night.
"Today we lost a friend, a mentor and a great visionary," Glenn Murphy, chief executive and chairman of Gap Inc., said in a statement.
"Don and Doris took a simple idea and turned it into a brand recognized as a cultural icon throughout the world and changed the face of retail forever."
A former real estate developer, Fisher switched to retailing at age 41 after he tried to return a pair of ill-fitting jeans at a local department store. Finding the store messy and its selection of sizes and styles limited, Fisher decided he could do better.
With $63,000 in capital, the Fishers came up with a concept for a store that would feature a broad selection of Levi's, neatly arranged by size in wall cubicles rather than stacked haphazardly on tables.
The Fishers opened their first store on Ocean Avenue in San Francisco on Aug. 21, 1969. The name "The Gap" was suggested by Doris Fisher as a reference to the "generation gap" that was widening in America during the late 1960s. (They initially considered Pants and Discs, because the first store sold records and tapes in addition to Levi's.)
The company expanded throughout the 1970s and '80s, and its "Fall into the Gap" became one of the more enduring American advertising slogans. Over the years it added offshoot brands such as BabyGap and GapKids, as well as the Banana Republic and Old Navy chains.
By the time Fisher stepped down as chief executive in 1995, the Gap was a fashion trendsetter and retailing powerhouse. The brand held so much cachet that actress Sharon Stone paired a Gap T-shirt with a floor-length black skirt at the 1996 Academy Awards.
But the company has faltered in the new millennium as competitors multiplied, and it struggled to cope with rapid expansion and changing fashion tastes. Fisher retired as chairman in 2004, and the company's sales peaked that year at $16.27 billion.
Since then, the company has closed some stores and dropped unsuccessful concepts such as Forth & Towne, a clothing chain aimed at baby boomers. The company now operates about 3,100 stores, including in Canada, Britain, France and Japan. Sales last year were $14.53 billion.
Fisher remained a member of the Gap board and held the title of chairman emeritus until his death.
Born Sept. 3, 1928, in San Francisco, Fisher received a bachelor's degree in 1950 from UC Berkeley, where he was a star swimmer and water polo player.
Fisher was a noted art collector and philanthropist. He was active in the Bay Area United Way and, along with his wife, founded the KIPP Foundation, a network of free, open-enrollment college-prep schools. Over the years, the Fishers provided $100 million to the foundation and to Teach for America, the company said.
He also served on the board of the San Francisco Museum of Modern Art, which will house his world-class collection of contemporary art.
In addition to his wife, Fisher is survived by their three sons and 10 grandchildren; and two brothers, Jim and Bob Fisher.
His son Bob Fisher continues to serve on Gap's board of directors, and Doris Fisher serves as an honorary lifetime member of the board.