Sculpture is the best comment a painter can make on his paintings,” said Picasso. “A drawing is a sculpture,” said Matisse. “White paint is my marble,” says Cy Twombly. During the past hundred years, unprecedentedly, great painters collapsed traditional boundaries between media by making sculptures as complements to their canvases, experimenting, innovating, working through formal issues. Their adventures into plastic art are the subject of this summer’s must-see exhibition, Sculpture by Painters at Baden-Baden’s Frieder Burda Museum: the most stunning, seductive, stimulating show I have encountered in Europe this year.

Cherry-picking 150 masterpieces – many rarely seen and privately owned, others iconic – Jean-Louis Prat has drawn on half a century as curator and friend of artists including Miró, Giacometti and Chagall to orchestrate a dizzying set of dialogues. You arrive via Jean Dubuffet’s chunky, three-metre, paint-splattered polyurethane “Tour Ballerine” (1974), a graffiti monument at the entrance. Once inside, you realise that it is in conversation both with Degas’ bronze and muslin-tutued “Little Dancer” (1880-81), a work conveying with yet more spontaneity than the artist’s impressionist paintings the forcefulness and tension of movement, and with Max Beckmann’s bold expressionist bronzes “The Dancer” (1934) and “Crouching Woman” (1935), which look as if they have been detached – isolated and wary of the space around them – from Beckmann’s doom-laden mythological canvases.

Prat curates with a light touch, deep scholarship and a frisson of anarchy. In an opening juxtaposition, de Kooning’s fleshy, extravagant, huge-limbed “The Clamdigger” (1972), all rippling surfaces and bursting matter, thunders at disappearing Giacomettis such as the exquisite “Figurine Between Two Houses” (1950), an image of postwar flight and claustrophobia. Yves Klein’s blue-pigmented male nude on gold leaf, “Portrait-relief d’Arman” (1962) debates materiality and pictures-as-objects with Antoni Tàpies’ weather-beaten, monochrome “Interlaced Material” (2004), thick with sand, resin and powdered marble. Max Ernst’s cerebral eroticism (“Lunar Asparagus”, a pair of spindly creatures whose faces are comic genitalia) sets off Joan Miró’s playful sensuality (the painted, high-heeled mannequin and tap comprising “Jeune fille s’évadant”): twin poles – both made in 1967 – of late surrealist incongruity.

Cumulatively, each piece unfolds the story of how modernism’s metamorphoses of forms and matter scrapped art’s hierarchies to create the plurality of expression and liberal definition of sculpture that we take for granted today. The contemporary resonance is enhanced by Richard Meier’s aluminium and glass museum, its giant blinds filtering natural light deliciously across all floors through three-storey windows. This starry building put Baden-Baden on the European art map in 2004; it works to particularly fine effect in symbiosis with the colour and light of late 19th- and early 20th-century art.

“She was a pretty girl, a perfect model. I touched her body, my hands enveloped her forms, and I transmitted into earth the equivalent of my sensation,” Matisse wrote of his work as sculptor. More tactile, sexualised and distorted than his drawings or paintings, his bronzes – such as the monumental series “The Back”, begun simultaneously with the radical “Dance” and “Music” canvases of 1909-10, the mask-like “Jeannette”, the harshly foreshortened “Two Negresses”, and the lumpy, agitated “The Serf”, for which Matisse borrowed Rodin’s ageing stocky giant of a model Bevilaqua for more than 300 sittings – have a terribilità and aggression that still unnerve. Shown here with uneasy early nude studies in blistering colour such as “Nude with Pink Shoes” and “Still Life with Ivy”, Matisse’s sculptures underline his lifetime struggle with grounding figures in space – a struggle less apparent, though still underpinning, the taut harmonies of his later paintings.

Each pioneer of modernism here had his own use for sculpture. Ernst Ludwig Kirchner’s experiments in rough-surfaced angular nudes carved in wood, their fragmented bodies jagged and doll-like, inform the brutally erotic nudes, painted in livid cerise, orange, lime green, that dominate his first expressionist canvases. Modigliani began his career as a stone carver, turning to painting when stone dust damaged his lungs, already weakened by the tuberculosis that would kill him at 35. His elongated stone female heads, with their closed almond eyes and serpentine necks, stand here alongside the paintings whose sculptural forms they influenced, but “he painted only faute de mieux”, recalled a friend; “his veritable passion was to work in stone.”

At the same time, away from the glare of the public, Picasso, whose first sculpture show did not take place until 1966, made the medium a testing ground for his most charged ideas from 1906 on. These range from the breakdown of solid volume into shifting masses that anticipated cubism’s varying perspectives, in early heads depicting his companion Fernande, to the assemblages of the 1950s and 1960s, such as the sheet-metal, double-headed “Tête de Femme” – raw, vital, modelled on his wife Jacqueline’s strong aquiline features – a rusted “Femme debout”, a wooden “Tête de Taureau”. Playing on the not-quite-complete transformation of banal object or material into artwork, these show Picasso alert to every nuance of art’s postwar democratisation.

If sculpture before 1914 offered a direct link to primitivism – African statuary, folk objects, stone steles – it became in the postwar epoch also an escape from staleness as the modernist generation entered middle-age. Chagall, after a seven-year lacuna in which his wife died and then his young mistress left him, was at a creative impasse when he moved to the south of France and in 1952 began experimenting with the Provençal craft of ceramics. Its textures, and purification of colour by fire, immediately fed the revival of his painting. His most important postwar canvas is “Clowns at Night” (1957), where a band of circus performers – Chagallian analogy for the artist – wander across a dark field under two sinister moons. It has a blackish-blue ground enlivened by muted colour accents encrusted into a thick, granulated, earthy surface: the influence of modelling and engraving clay, which Chagall called an art of the earth, is clear.

Just as poignant is the way his bronzes from 1952-53 give new life to key images from his early oeuvre. The simplified “Virgin with Child” reasserts the theme of maternity. “La bête fantastique”, a fabulous, energetic creature inset with a pair of lovers, recalls the blazing, mythical man-and-beast of Chagall’s primitivist “The Cattle Dealer” 40 years before. In a luminous marble woman’s head draped over a horse, “Sculpture colonne” of 1953, east European Hasidic myths of the interdependence of man and beast are transformed into an art of French formalism, underlining the reinventions on which Chagall’s art depended.

In the 1940s and 1950s, the survivors of the Ecole de Paris lined up along the Côte d’Azur – Picasso, Matisse, Chagall, Léger and Dufy lived there, while Braque had summer quarters. There were rivalries – Picasso once maliciously completed a ceramic “à la Chagall” that the Russian had left unfinished at the Vallauris pottery studio where both worked; Braque visited an exhibition of Picasso’s ceramics and left with the single crushing remark “it’s well-cooked” – but all were in the same game of reasserting late modernism’s connection with Mediterranean classicism. Braque’s Greek-inspired animal bronzes, such as the greying “Grande tête de cheval”, parallel his magnificent, pared-down grey canvases – “La Nuit” is displayed with it here – and show, said sculptor Henri Laurens, “a painter turned sculptor by the curiosity of seeing what was really happening behind his picture”. Braque admitted that sculpture was a way of “losing the habit of painting – it’s very important for a painter to combat habit”. This thoughtful show unfolds surprises in the work of great 20th-century artists; its triumph is to combat our own familiarity with the modernist experiment and to make it relevant again to our own age.

‘Sculpture by Painters’, Museum Frieder Burda, Baden-Baden, until October 26. Tel: +49 7221 398980; www.museum-frieder-burda.de