The attraction was the second exhibit to open at the zoo in 1936, the Chicago Tribune said. The exhibit once housed 70 animals.
The zoo announced Friday that it had closed the exhibit to make room for a new attraction, which hasn't been announced.
The decision came after the zoo euthanized the last three animals on Sept. 12 for quality of life concerns.
The zoo stopped breeding the baboons in 1992 and, as a result, the island's animal population decreased over the last two decades, the Tribune said.
Demolition of the island is scheduled to take place in 2014, and a spokesman said the new attraction is under review.