Williams lost 6-4 6-3 to Svitolina, ranked 20th in the world.
Williams and sister Venus were knocked out of the women’s doubles on Sunday by Czech Republic pair Lucie Safarova and Barbora Strycova.
Svitolina, who will face the Czech Republic’s Petra Kvitova in the quarter-finals, said: “It’s an unreal feeling for me. This is just a perfect moment.”
Williams follows men’s top seed Novak Djokovic inexiting the Olympics after he was defeated in both singles and doubles.
The 34-year-old’s exit means Angelique Kerber and Madison Keys are the only top-eight seeds remaining of what had appeared a very strong field.