It sure as hell got under mine. Jonathan Glazer's sci-fi horror is loosely adapted, or atmospherically distilled, by Walter Campbell from the 2000 novel by Michel Faber. The result is visually stunning and deeply disturbing: very freaky, very scary and very erotic. It also comes with a dog-whistle of absurdist humour that I suspect has been inaudible for some American reviewers on the international festival circuit so far.

The heroine is an alien predator at large in Scotland. Maybe you have to be a Scot, or anyway a Brit, to appreciate Glazer's masterstroke in casting Scarlett Johansson as the exotic alien in humanoid form, with her soft London accent, tousled black wig and sexy fake fur, driving a knackered white van around the tough streets of Glasgow, picking up men. She winds down the passenger-side window, artlessly engages them in conversation, and takes them back to her place. Between encounters, she roams, gazing at streetscapes, and making them alien with that gaze – like a Craig Raine poem. At one stage, she and her van are surrounded by guys with Celtic scarves. She is the ultimate Rangers supporter.

There is pure situationist genius in the bizarre spectacle of sleek Johansson being placed in this context, with lots of hidden-camera shots of real passers-by in real Glasgow streets and real Glasgow shopping centres, all these people being coolly sized up and assessed for their calorific value. From these genuine crowds, professional actors will seamlessly emerge for dialogue scenes. You can never forget it is Johansson on the screen, and that is surely the point. A Hollywood A-lister is as much of an alien here as any extraterrestrial from a flying saucer. (The final credits reveal that as well as a personal assistant, Johansson had a "personal security" team. I wonder if they were called upon at any point.) Her alien is voluptuous, superbly insouciant, unaffected by her surroundings – though I think feeling the cold a tiny bit. She greets the stunned menfolk with an unreadably polite half-smile. This is how I imagine Elizabeth Taylor to have looked and behaved when Richard Burton first took her to Port Talbot.

The story of Johansson's alien begins with a mysterious and Kubrickian "birth" scene in a brilliantly rendered dimensionless otherworld. The alien is transferred to Scotland's dark, rainy streets and it – she – appears to have a minder, who rides a motorbike, and secures for her a human bodyshape from a dead girl retrieved from the roadside. Or perhaps that is another expired alien whose shape is being reused. At any rate, our alien is soon up and running in her Ford Transit, seducing wide-eyed males who can't believe their good luck and are quite right not to.

At the seashore, she witnesses a complex "rescue" scene in which earthling emotions of pity and compassion are on display – feelings she does not share. The most staggering scene is one in which the alien picks up a young man with the facial disfigurement of neurofibromatosis, played by Adam Pearson. The alien does not essentially distinguish between his looks and those of her other victims, but there is a crisis, and the alien becomes vulnerable: a potential victim herself.

Under the Skin

Glazer has stylishly absorbed the influences of Nic Roeg and David Lynch, with something of Gaspar Noé in the hardcore moments and maybe an echo of Bertrand Tavernier's Glasgow film Death Watch. There are memories of An American Werewolf in London and even, in the alien's loneliness, a touch of ET. But Glazer places his film in such a different and unexpected locale: in tough city streets more associated with Andrea Arnold or Ken Loach. The quicksilver shapes of futurist bodyhorror fantasy are scuffed with social-realist grit, but modified, too, with Jonathan Glazer's brilliant flair for visual impact. And I'm someone who still watches this director's horses-in-the-surf Guinness commercial on YouTube and gasps. His previous films Sexy Beast (2000) and Birth (2004) had more conventional twisty plots. This is a pure intravenous injection of mood.

And what is that alien doing anyway? Just eating? Or is she the advance party of a colonising power that has conquered England and is coming north? Johansson's alien has clearly hit a Hadrian's Wall of trouble in these misty lands and found that the Scots are not so easy to subdue.

At the press screening, the final credits were greeted by a sudden nasal exhalation from us critics: the sound of people realising they have been holding their breath. It's the equivalent of regular audiences jumping to their feet and applauding.

• Interview: Jonathan Glazer on why the film took a decade to make