There could be no more refreshing tonic to counteract the commercial excesses of last week’s Frieze Art Fair than the free new exhibition at the Fitzwilliam Museum in Cambridge. Meticulously displayed and full of radiant masterpieces, Vermeer’s Women: Secrets and Silence had me rapt from the start.

Only four of its 32 paintings are actually by the master of Delft who headlines the exhibition — but given that only around three dozen works by Vermeer are known today, this isn’t a bad hit rate. The star of the show is unquestionably Vermeer’s The Lacemaker, on loan from the Louvre, and displayed in Britain for the first time. Scrutinising this enigmatic, jewel-like painting in the context of related works by Vermeer’s contemporaries only enhances its lustre.

The exhibition concentrates on a popular strand of Dutch genre painting in the second half of the 17th century: pictures featuring women within domestic settings. In canvas after canvas, we see maidservants and well-to-do housewives performing mundane tasks: sewing, spinning, fetching water, scraping parsnips, shedding stockings, breastfeeding, playing the virginal — even, in one rare example, reading a book. The interiors are usually spick and span, reflecting the Dutch mania for cleanliness and order, and often full of exquisitely rendered luxuries, such as expansive patterned marble floors and expensive paintings and rugs, which bespeak the prosperity of the households being depicted.

On reflection, it may seem strange that such scenes should continue to fascinate us. We can readily understand why they were desirable in their own time: as the curator Marjorie E Wieseman points out in the excellent catalogue, the vogue for painting middle-class interiors coincided with a period of peace and prosperity in the wake of the Treaty of Münster in 1648, when the United Provinces of the Netherlands secured independence from Spain following the Thirty Years War. For the Dutch, pictures of neat-and-tidy households were patriotic affirmations of a buoyant new nation run by wealthy merchants rather than monarchs.

Today, though, it would be tempting to dismiss such images as nothing but the material obsessions of a preening, house-proud bourgeoisie. Many of these paintings, after all, seem to be about showing off. Gerrit Dou’s overblown Woman at her Toilet of 1667, for instance, contains a multitude of recherché stuff: sumptuous clothes and textiles, glinting pearls, a gilt-framed mirror. This is a painting about self-infatuation — not only that of the mistress of the house, who flirts with us via her reflection in the mirror at its centre, but also on the part of the artist, who descants his virtuosic ability to capture an impressive array of surfaces and textures. By the same token, why should we give a fig for the woman in a painting by Quiringh van Brekelenkam who, decked out in satin finery, inspects a tray of fish offered to her by a maid, signalling her efficient command over her household?

Yet, curiously, we do care about these women. This is not because we are presented with tranquil snapshots of “real” life — we know that Dutch artists wilfully manipulated the layout and décor of the houses they painted to suit their compositions. Rather, it is because the best paintings in this exhibition radiate a hushed intensity — the intensity of someone concentrating hard on a particular activity, as in Nicolaes Maes’s A Young Woman Sewing of 1655, or the lady who absentmindedly sips from a wineglass while ruminating over the contents of the missive in her right hand in Woman Reading a Letter by Gerard ter Borch (who was, incidentally, a master at capturing the silvery shimmer of white satin). In several pictures, you can almost hear the lethargic tick of a pendulum clock just out of view, or trace the languid orbit of dust-motes in the sunlight streaming through the leaded glass windows. These paintings are the antithesis of the hubbub of modern life — hence their bewitching appeal.

Nobody summons this quality of silence and slow time more subtly than Johannes Vermeer. Unlike Dou, he doesn’t bend over backwards to engage the viewer’s attention. He refrains from signposting the purity or prudence of the women in his spare paintings, and never broadcasts his own virtuosity in a boorish fashion.

In The Lacemaker, a late work from around 1670, he excises theatrics and a sense of narrative altogether. There is no simpering or showing off here. Instead, Vermeer offers us a serenely self-absorbed young woman, forever indifferent to our presence. She does not come to us; we must go to her. This creates a persuasive sense of her interior life thrumming away as she works. Dressed differently, she could be our contemporary.

Moreover, her concentration is a metaphor for Vermeer’s painstaking application of paint. Certain passages to the left of the composition are almost abstract — such as the splashes of white and red representing coloured threads that cascade like miniature waterfalls from the blue sewing cushion. This is an image of profound stillness and beauty.