Klein, a Serbian-born designer who died in 2014, collaborated with major European fashion houses such as Dior to design some of the most beautiful textiles of the 20th century.
His studio was built as a workspace for design, weaving and exhibiting samples.
It lies adjacent to his home, High Sunderland, built by Womersley in 1958 and also a listed building.
Historic Environment Scotland (HES) describes the studio as a “very fine sculptural late Modernist building designed by Peter Womersley”.
It says the building was designed to connect harmoniously with its setting on the sloping wooded site.
The severe horizontality of the concrete elements succeed in contrasting with the verticals of the trees around it, HES says.
The property is being auctioned by Savills, which describes it as in need of modernisation, with further potential, “subject to requisite consents”.
“It remains a masterpiece of structural elegance integrated into its wooded landscape,” Savills say.
Womersley other works include Netherdale, the football stadium, external he designed for Gala Fairydean FC in 1963, the boiler house of the former Dingleton Hospital in Melrose and part of Edinburgh’s Western General Hospital.