Arnold Jacob Auerbach was one of the four children of Marie and Hyman Auerbach. Hyman was a Russian-Jewish immigrant from Minsk, Russia, and Marie Auerbach, nee Thompson, was American-born. Auerbach Sr. had left Russia when he was 13, and the couple owned a delicatessen store and later went into the dry-cleaning business. Little Arnold spent his whole childhood in Williamsburg, Brooklyn, playing basketball.

Auerbach was one of four children of American-born Marie Auerbach and Russian Jewish immigrant Hyman Auerbach in Brooklyn. His brother Zang Auerbach, four years his junior, was a respected cartoonist and portraitist at the Washington Star. He married Dorothy Lewis in the spring of 1941. The couple had two daughters, Nancy and Randy.  Auerbach was known for his love for cigar smoking. Because Red made his victory cigars a cult in the 1960s, Boston restaurants would often say "no cigar or pipe smoking, except for Red Auerbach". In addition, Auerbach was well known for his love of Chinese food. In an interview shortly before his death, he explained that since the 1950s, Chinese takeout was the most convenient nutrition: back then, NBA teams travelled on regular flights and had a tight time schedule, so filling up the stomach with heavier non-Chinese food meant wasting time and risking travel-sickness. Over the years, Auerbach became so fond of this food that he even became a part-owner of a Chinese restaurant in Boston. Despite a heart operation, he remained active in his 80s, playing racquetball and making frequent public appearances.  Despite his fierce nature, Auerbach was popular among his players. He recalled that on his 75th birthday party, 45 of his former players showed up; and when he turned 80, his perennial 1960s victim Wilt Chamberlain showed up, a gesture which Auerbach dearly appreciated.  In an interview with ESPN, Auerbach stated that his all-star fantasy team would consist of Bill Russell--who in the former's opinion was the ultimate player to start a franchise with--as well as Bob Pettit, Elgin Baylor, Oscar Robertson and Jerry West, with John Havlicek as the sixth man. Regarding greatest basketballers of all time, Auerbach's candidates were Russell, Larry Bird, Magic Johnson, Kareem Abdul-Jabbar, Michael Jordan, and Robertson."

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He recalled that on his 75th birthday party, 45 of his former players showed up;