The Aspen Art Museum is getting ready to attempt the art-world equivalent of a double black diamond.

After three decades of shoehorning contemporary-art exhibits into a former power plant on the outskirts of this wealthy Rocky Mountain enclave, the museum plans to triple its footprint. It will relocate in August to a new home designed by Pritzker prize winner Shigeru Ban in the center of town—a move that illustrates the growing clout and ambition of Aspen's stewards.

Mr. Ban, who is known for using unconventional materials like paper and cardboard tubes, has created a three-story building that resembles an enormous wooden crate. The 33,000-square-foot facility, which opens Aug. 9, has walls of wood veneer planks woven into latticework. The grid covers a glass wall, giving passersby a glimpse inside.