At a press conference in Denpasar on Monday, police chief Sr. Comr. Ruddi Setiawan said Zhestko was on his way to Russia.
The animals only exist on two islands -- Sumatra and Borneo -- with habitat loss and illegal logging contributing to most deaths in the wild.
Speaking to the Jakarta Post on Saturday, Dewa Delanata, head of the airport's quarantine office, said Zhestkov was accused of "deliberately using an inhumane method" to allegedly smuggle the two-year-old orangutan.
"At first, we thought it was a monkey. The officers were afraid to open the basket as they thought the monkey would be aggressive and run loose in the departure area," Dewa said.