Fisher opened the first Gap store with his wife 40 years ago, after a frustrating experience exchanging a pair of jeans that didn't fit.
Leaving behind a career in real estate development, the then 41-year-old Fisher and his wife Doris believed that opportunities existed for a retail company that could provide consumers with a variety of fit and style options, so they raised $63,000 to launch a single jeans and music store called The Gap (named for "the generation gap") in San Francisco.
A life-long resident of San Francisco, Fisher was often credited with inventing the speciality retail category, although he was equally known for his commitment to philanthropic and civic activities.
Glenn Murphy, chief exectuive and chairman of the board of Gap, now one of the world's most famous high-street fashion brands, said: "Today we lost a friend, a mentor and a great visionary.
"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. We will miss him deeply, and our thoughts and prayers are with Doris and the entire Fisher family during this time."
From its inception in 1969 through to 1995, Fisher held the roles of Gap chairman and chief executive. During this period, Gap expanded to include the Banana Republic, GapKids, babyGap, and Old Navy brands in addition to a growing international presence in the UK and Canada.
In 1995, he relinquished his chief executive position but retained his leadership of the board. In 2004, he stepped down as chairman but continued as a company director and executive in the role of founder and chairman emeritus, which he held until his death.
Fisher's son Bob, who served as Gap's chairman from 2004 to 2007, said: "My father was an inspiration to many people both in his dedication to his business and through his enthusiasm and commitment to philanthropic efforts.
"On behalf of our family, we want to thank everyone who has offered their love and support. We are comforted in the knowledge that my father's legacy will live on in the spirit and passion of the millions of people who have worked over the past 40 years for the company he founded."
Today, Gap has annual sales of about $14.5bn (in fiscal 2008) and offers clothing, accessories and personal care products for men, women, children and babies.
It operates more than 3,100 stores in the US, the UK, Canada, France, Japan and Ireland.