Nobody familiar with the work of Rei Kawakubo would question that her designs merit a showcase in a museum or gallery.

Under Comme des Garçons label she founded in 1969, the abstract, architectural creations by the 74-year-old Japanese designer resemble sculptures.

It comes as little surprise that the New York Metropolitan Museum Costume Institute’s exhibition of her work, Rei Kawakubo/Comme des Garçons: the Art of the In-Between, which opens to the public on Thursday, is as avant-garde as the collections that have cemented her reputation.

Kawakubo is the first designer to be celebrated with an exhibition by the museum while still alive since Yves Saint Laurent in 1983.

“Since her first show in Paris in 1981, Kawakubo has consistently surprised us and disrupted our expectations,” said Andrew Bolton, curator of the Costume Institute. “Season after season, collection after collection, she changes our eye by upending perceived notions of conventional beauty.”

The Art of the In-Between has nine themes of dualisms, including Absence/Presence, High/Low, Fashion/Antifashion and Object/Subject, and opens with five red garments, including two body-con dresses from her groundbreaking spring/summer 1997 collection Body meets Dress – Dress Meets Body, which used hybrid bodies and played with notions of deformity, and two oversized structural jackets from her autumn/winter 2012-13 collection 2 Dimensions.

Fashion/Antifashion focuses on Kawakubo’s early 1980s collections, which drew extreme reactions from critics when first shown on the catwalk in Paris. Viewed more than 30 years on, the all-black collections – which challenged traditional fashion orthodoxies with their asymmetry, deconstruction, draping, and plays on proportions – not only now seem wearable but perfectly demonstrate the designer’s impact on fashion aesthetics.

Other works are anything but wearable (“Personally, I don’t care about function at all,” Kawakubo declared previously); Clothes/Not Clothes features many examples of her desire to produce ‘objects for the body’, with cartoonish silhouettes and extravagant proportions more reminiscent of doll’s clothing or theatrical costume than fashion, and giant, ghoulish confections of lace, embroidery, silk and feathers.

The exhibition is housed in a minimalist maze-like space with arches, podiums and elevated galleries, which was designed by Kawakubo in conjunction with the museum. “I would find it impossible to see my clothes in a space designed by someone else,” she told Bolton. ‘My clothes and the space they inhabit are inseparable.”

There are, bar one large glass box suspended at 20 ft, no cases or barriers separating visitors from the designs. The famously private designer rarely grants interviews, does not even take a bow to close her shows, and has never before attended a Met Gala, the lavish fashion party that marks the opening of the annual exhibition – however, she was due to attend for the first time on Monday night.

Kawakubo prefers to let the clothes speak for themselves, and the exhibition is free of labels or plaques, with only numbers on the floor beside each item to identify them.

“We made the conscious decision not include any text in the show, but instead to present it in a booklet that visitors can read if they so wish,” Bolton said. “We wanted people to engage with Rei’s fashions on a more personal and intimate level.”

Blurring boundaries of gender and culture, Kawakubo’s designs combine masculine and feminine clothing traditions, as well as east and west, in garments that are not about a flattering fit or flaunting physical assets.

Just 15 blocks from Trump Tower, there could be no better place or time to celebrate an iconoclast whose work rejects the objectification of the female form.

Rei Kawakubo/Comme des Garçons: the Art of the In-Between opens on 4 May to 4 September at the Metropolitan Museum of Art’s Costume Institute in New York