Minkoff was born on August 11, 1962 in Palo Alto, California. He studied at Palo Alto High School and graduated from California Institute of the Arts in the early 1980s in the Character Animation department. While he was working his way through CalArts, he was hired by Walt Disney Animation Studios in 1983 as an in-between Artist for The Black Cauldron (1985). He was then a supervising Animator for The Great Mouse Detective (1986), before being a character designer for The Brave Little Toaster (1987). He also wrote the song "Good Company" for Oliver & Company (1988), before becoming a character Animator for The Little Mermaid (1989). He then became a Director for two Roger Rabbit shorts called Tummy Trouble (1989) and Roller Coaster Rabbit (1990) and was a part of a pre-production script development for Beauty and the Beast (1991). He also directed a Mickey Mouse short, which was shown at Disney-MGM Studios, called Mickey's Audition (1992).
Minkoff got his big break when he directed the Walt Disney Animation Studios feature film The Lion King (1994) alongside Roger Allers. Since then, he has directed his first live-action movies Stuart Little (1999) Stuart Little 2 (2002), which were a mix of live action and computer animation, and then some fully live action movies like The Haunted Mansion (2003), The Forbidden Kingdom (2008) and Flypaper (2011).
Minkoff married Crystal Kung on September 29, 2007. They met in 2003 at a party in Minkoff's office.
He directed DreamWorks Animation's computer-animated film Mr. Peabody & Sherman. He is also attached to direct the fantasy action adventure Chinese Odyssey. As of 2014, he is producing Blazing Samurai, an animated family film inspired by Blazing Saddles and scheduled for a 2017 release. Minkoff is also a Director on the 2018 animated Netflix original animated series of the late Anna Dewdney picture book franchise Llama Llama, overseeing all aspects of production.
