Inokuma was born in Yokosuka, Kanagawa, and began judo at age 15. He entered the Tokyo University of Education (current University of Tsukuba) and won the All-Japan Judo Championships in 1959 at only 21 years of age to become the first student competitor to win the championship. He placed second in the All-Japan Championships from 1960–1961, facing future Olympic silver medalist and lifelong friend Akio Kaminaga in the finals both years.
Inokuma won the 1963 All-Japan Championships, but placed 4th in the 1964 All-Japan Championships and ended up entering the 1964 Summer Olympics in the +80 kg division (the heaviest weight category at the time excluding the Open category). In the Olympic final he defeated Canadian judoka Doug Rogers with an Ippon Seoinage to win the gold medal. His victory came after recovering from a hip injury caused by overwork, and Rogers was over 30 kg heavier than Inokuma at the time of the match.
After graduating, Inokuma became a judo instructor for Juntendo University and the Tokyo Metropolitan Police Department. In 1965, he entered the Open weight class of the World Judo Championships intending to face Dutch judo champion Anton Geesink, but Geesink had entered in the +80 kg division that year, and the two never faced off against one another. Both Geesink and Inokuma won gold medals in the competition, and Inokuma announced his retirement shortly afterwards, citing lack of motivation.
In 1966, he resigned from his post at the Tokyo Police Department to become an executive at the Tokai Construction company. He continued to work with judo as an advisor for the International Judo Federation, and as an instructor at Tokai University, where he coached future Olympic gold medalist Yasuhiro Yamashita. He also authored several prominent books and manuals relating to judo, contributing to the sport's development. He became the CEO of the Tokai Kensetsu company in 1993, but committed suicide in 2001 by means of seppuku, possibly due to the financial losses suffered by his company. He was 63 years old.