Hoffman is from an Ashkenazi Jewish family of immigrants from Ukraine and Romania.
Hoffman was born on August 8, 1937 in Los Angeles, California, the second son of Lillian (née Gold; 1909–1982) and Harry Hoffman (1908–1987). His father worked as a prop supervisor (set decorator) at Columbia Pictures before becoming a furniture salesman.
Hoffman was named after stage and silent screen actor, Dustin Farnum. His elder brother, Ronald, is a lawyer and economist. Hoffman is Jewish, from an Ashkenazi Jewish family of immigrants from Kiev, Russian Empire, and Iași, Romania (the family's surname was spelled "Goikhman" in the Russian Empire). He does not speak Yiddish.