"Surely," a desperate character muses on his way to court, "there were a thousand other men like him who'd made mistakes enough to ruin their lives, their careers and their families, and yet surely those men had carried on, as had their families. There was room for everything in this vast, disordered place."

The place is Jeddah, Saudi Arabia, depicted by Zoë Ferraris with sympathy and realism, and in all its complexity: through its text messages and mobiles, SUVs and shopping malls, its exorcist surgeries and women-only banks, plus the "forced meditation" of compulsory prayer and the harsh worlds inhabited by immigrant workers. Both female and male, these constitute perhaps a third of the Saudi population, and they give this novel its title.

To start with, 19 bodies are found in the desert. The carefully mutilated victims are immigrant women, Asians, and their corpses are arranged to convey a hidden message. Enter Chief Inspector Ibrahim Zahrani, whose repertoire includes policeman's intuition and Bedouin trackers as well as forensic analysts and an American expert on serial killers.

Ibrahim is a liberal in his context, a rationalist, but he's not squeamish about applying violence to the deserving. In Ibrahim's book, "fierce, dignified personal power" is "the most highly regarded quality in a woman". His wife Jamilah has other ideas, and spends her time busily arranging unsuitable marriages for their children. One such deal has paired her son with Saffaneh, whose "version of religion" ruffles Ibrahim's feathers. But Saffaneh's puritanism hides a secret.

Ibrahim is also hiding something: his lover Sabria, an Asian immigrant, once an abused housemaid, and another bearer of secrets, has gone missing. For obvious reasons  the draconian Saudi adultery law, for example  Ibrahim can't talk about it.

Except to Katya Hijazi, the novel's Saudi heroine, who works in forensics but aspires to the man's world of the homicide department. Her status as a working woman may be suspect, and she is not permitted to drive herself around, but Katya does much of the legwork and most of the puzzle-solving. She enacts the detective's readerly habit of making connections and penetrating the mind of the psychopath. In all this, she is assisted by dreams, and by her detective's gaze which, like the writer's, is able to tease out histories from clues, to illuminate a life from its furniture.

She follows leads through bourgeois Saudi sitting rooms into impoverished shanty towns inhabited by people who've overstayed their Haj visas, maids fled from slavery and rape, those who don't have their employer's permission to leave.

The narrative moves smoothly between Ibrahim and Katya's perspectives, and drifts into other minds too. Nayir, Katya's fiancé, who inevitably becomes her chaperone and driver, is a well drawn conservative-liberal, a clash of tradition and modernity: a very ordinary Saudi, in other words. Katya and Nayir own the book's final scene, and their end is both more convincing and raises more questions than Ibrahim's.

Ferraris's acute psychological observations bring her characters to life, and she has an unerring sense of place and (better still) of time. Her Jeddah is concrete rather than exotic, real enough to feel like a shimmering moment, with the ever-present process of social change communicated by subtle detail and the characters' shifting thoughts. Replete with bad cops, false leads, twists and sudden turns, this is superlative crime fiction mixed with unforced cultural analysis that bursts right out of genre constrictions.

 Robin Yassin-Kassab's The Road to Damascus is published by Penguin.