Pham Van Tan, director of the Saigon Zoo and Botanical Gardens, confirmed the incident Saturday.
The Borneo orangutan lives alone inside a semi-wild enclosure for primates in the zoo.
Tan said orangutans are intelligent creatures who may imitate human actions, but did not explain how this one got its hands on a lit cigarette.
Some visitors neglected notices and threw food and trash into the enclosures, he said.
Borneo orangutans are listed as a critically endangered species by the International Union for Conservation for Nature due to the loss of their natural habitat and hunting.
The Saigon Zoo and Botanical Garden, opened in 1864, is among the world's 10 oldest zoos.