Klein went to Isobel Rooney Middle School 80 (M.S.80) as a child. He attended the High School of Art and Design in Manhattan and matriculated at, but never graduated from, New York's Fashion Institute of Technology, receiving an honorary doctorate in 2003. He did his apprenticeship in 1962 at an old line cloak-and-suit manufacturer, Dan Millstein, and spent five years designing at other New York City shops. In 1968, he launched his first company with a childhood friend, Barry K. Schwartz.
In 2003, Klein bought an ocean-front estate in Southampton, New York on Long Island and demolished it to build a $75 million glass-and-concrete mansion. In 2015, he put his Miami Beach, Florida mansion on the market for $16 million. The Florida home sold in February 2017 for $12,850,000. In June 2015, Klein bought a mansion in Los Angeles, California for $25 million.