The fast show: Italy's Enzo Ferrari Museum is a fitting memorial to its maverick creator

Jan Kaplicky knew how to fail, brilliantly, better than any other architect in the 21st century. The practice that he and Amanda Levete ran in London's swish Holland Park was called Future Systems, and it became famous for losing architectural competitions with building designs that ranged from gleaming amoebas to towering, ribbed condoms. Even so, they delivered two of Britain's most extrovert buildings, the periscopic Lord's Media Centre, and the glittering supersized basque known as Birmingham's Selfridges.

Kaplicky's final building, the Enzo Ferrari Museum in Modena, has just been completed by his protégé, Andrea Morgante and his London-based practice, Shiro Studio. Kaplicky's fascination with cars and big, big toys for big, big boys is perfectly distilled in the museum's design: it's a giant sports car bonnet, a sleek, Modena yellow obituary to architecture's charming Mr Awkward, who dropped dead in a Prague street in 2009.

We may never see a building quite like this again. Its architecture comes from an imagination not of the future, but from Kaplicky's dream world, which was filled with the shapes of military aircraft, high-tech bits and bobs, and 1950s sci-fi magazines. The museum's shell suggests the sleek lines of a 1972 Ferrari Dino 246 GT, but also recalls spaceships on the covers of Astounding Science Fiction. Kaplicky was, as per the cover line on the May 1951 edition, a "galactic gadgeteer".

The museum is his finest gadget. And two things about the building are completely surprising. The museum, and the Ferrari family's beautifully restored original home and workshop next to it, cost the equivalent of £11.8m – which would barely secure a quarter share in an apartment at One Hyde Park.

Even more unexpected is the relationship of the museum's form with its urban context. A bright yellow building with 10 rooflights shaped like streamlined air-intakes should terrorise the mixture of architecturally calm 18th, 19th- and 20th-century buildings in this part of Modena. It doesn't. Why not? Firstly, because the building is half buried, with an aluminium roofline no higher than the ridge of Alfredo Ferrari's old metal-bashing workshop. Secondly, because the museum is simply graceful.

Simply being the key word. Andrea Morgante, who completed the project for the city of Modena after Jan Kaplicky's death, is apologetic about some of the building's details, and speaks wistfully of the kind of refinements seen in high-tech buildings by that master artificer of structural joints and connections, Nick Grimshaw.

Morgante's concerns are slightly misplaced: racing cars are pared-down machines, always on a knife-edge between design innovation and failure. When Norman Foster designed the TAG McLaren headquarters in Surrey, his proposals for wind-bracing struts were turned down: McLaren's boffins designed simpler ones. The architecture of the Enzo Ferrari Museum lacks that degree of ultra-refinement, but it succeeds in the most important way. Its form is more than an obvious metaphor for fast cars: the building looks, and feels, absolutely, a part of this stripped-down, high-performance world.

And Modena, after all, has been at the heart of motor racing since the 1920s, the city's workshops and factories turning out Alfa Romeos, Bugattis, Maseratis, Ferraris, and Lamborghinis. Enzo Ferrari drove for, and managed, Alfa Romeo before setting up his own motor racing company in 1940. The Enzo Ferrari Museum may not be the official Ferrari museum – that's in Maranello, 10 miles south – but it is still a cabinet of beautiful automotive curiosities, with 21 cars floating on thin platforms raised a metre above the floor.

Everything, apart from the cars and the yellow pods that contain the museum's shop and lavatories, is white. The interior is like the inside of a vast, high-tech oyster shell. And the cars – such as the cream 1948 Ferrari Barchetta, and the agate grey-blue 1955 Maserati Zagato Spyder – seem to have formed rather like multi-coloured pearls; automotive figments transformed from the nacreous grit of design ideas into gleamingly perfected high-speed machines.

It is hard to think of 21st-century motor racing as anything more than a sterilised video game populated with multi-brandmarked, baseball-hatted androids given to saying "for sure". But in this museum, we glimpse an age when cars screamed round the bumpy sopraelevata banking of the Monza track at 170mph on tyres that wouldn't be acceptable for a modern BMW family saloon. And Enzo Ferrari was a ruthless overlord of this world. "If he had been in politics," reports the motor-racing writer Joseph Dunn, "Machiavelli would have been his servant."

There's more than a touch of the sopraelevata to the museum's facade, a deliriously slanting double-curve of glass striated with horizontal louvers, engineered by Arup's Sean Billings. Each of the 30mm-thick steel-tension rods that lock the glass panels into position can take 20 tons of pressure caused by wind or snow. Jan Kaplicky conceived this part of the design as the radiator of a sports car – but that analogy doesn't work. The facade is much more like a windscreen that might have been designed by the Brazilian genius, Oscar Niemeyer.

Morgante cheerfully confirms that the design of the museum is an example of Kaplicky's pathological disinterest in design briefs: "Jan never cared about the briefs. He just liked to draw. He never designed options – the final design was always the evolution of the original sketch." Morgante made a significant contribution to the design, suggesting that the building "should be as if it was turgid and inflated, like a bonnet, and Jan agreed immediately."

Morgante describes the museum as a kind of hand that embraces the old Ferrari family buildings just 30 miles north of it. The metaphor won't do: the museum's form is paw-like, at best. It makes much more sense to think of the new and old buildings as history and modernity in vivid tension.

The architecture of the Enzo Ferrari Museum is the star of the show, but Morgante's design of the exhibition covering Enzo Ferrari's life, in the big barn-like ex-workshop, is a conceptually exquisite masterpiece. Morgante's idea was very simple: a pure white oblong with projecting fins that would suggest the pages of a three-dimensional biography of Enzo Ferrari, who was universally known as Il Commendatore.

Screens telling his life story are set back in the pages so that, as a whole, this oblong form radiates a wonderful, almost gorgeous, stillness. And high above this block of pages, two massive new white steel cross-braces – shades of tough, 19th-century engineering – hold the barn's walls together.

Andrea Morgante has delivered a very fine piece of restoration and exhibition design that is far more engrossing than Kaplicky's original idea for the space – a meandering red tifosi banner-cum-surface carrying images and artefacts from Enzo Ferrari's life. Morgante's approach has given the contents an interesting, slightly surreal piquancy. In all this white, perfectly sculpted purity, it comes as an amusing shock to gaze down into a small display vitrine and behold signor Ferrari's famous black-framed dark glasses.

The man who wore those glasses once said: "If you can dream it, you can do it." He also said aerodynamics are for people who can't build engines. The new museum has realised Modena's dream to sanctify its most famous son – even if some might give precedence to Modenesi such as Luciano Pavarotti, or the Vatican's senior exorcist, Gabriele Amorth. The museum also proves that, particularly here (and whether Il Commendatore's ghost likes it or not) aerodynamic form has a place in the architectural fabric of this city.