“Babygirl” isn’t a romantic comedy or a romance or even a comedy, though it concerns matters of the heart, and has a friskily impolite sense of humor. Set over what seems like a very long Christmas season, it centers on Romy — a transfixing Nicole Kidman — a married woman who enters a dominant-submissive affair that almost consumes her. It’s a story about women, bodies and the regulation of both, and what it means when a woman surrenders her most secret self. All of which is to say, it’s also about power, but with kinks.

Romy is the chief executive of a slick, growing robotics company that, from its videos, seems to provide warehouse automation. Presumably, the robots moving goods around will eventually make human labor redundant; in the meantime, they serve as a hard-working metaphor for a woman who’s rationalized every aspect of her existence. At her New York apartment, she dresses for another high-flying workday but then slips on a frowzy apron as she packs her children’s lunches with handwritten notes. (The lack of hired help is an off detail.) The apron seems so incongruent with her job and the frictionless perfection of her domestic realm that her puzzled husband, Jacob (Antonio Banderas), asks about it.

The writer-director Halina Reijn (“Bodies Bodies Bodies”) is just as scrupulously attentive to detail as Romy. With sensitivity to the gilded surfaces of Romy’s life, and with a series of brisk, narratively condensed scenes, the filmmaker sketches in a woman who presents an aspirational ideal, from her glossy lipstick to her teetering heels. Yet while the ceiling-to-floor windows of Romy’s importantly situated office announce that she’s a contemporary woman with nothing to hide, you know better: By the time Romy first breezes into work, you have already watched her sprint naked from her postcoital bed — where Jacob is sleeping the deep, contented sleep of the satiated — so she can secretly masturbate to online pornography.

The movie’s opener is a grabber — the first shot in the movie is a close-up of Romy seemingly on the orgasmic verge — and not only because Kidman bares her lovely, apple-cheeked rear as her character bolts down the hall. From the moment that the actress’s backside and coltish legs are gliding through the hushed darkness of Romy’s tastefully luxurious apartment, the movie seems to be invoking Stanley Kubrick’s 1999 erotic drama “Eyes Wide Shut.” In that hallucinatory film, which also opens at Christmas time, Kidman plays a married woman who sends her husband (Tom Cruise) spiraling after she tells him about her unconsummated desire for another man. “I was ready to give up everything,” she says.

In “Babygirl,” female desire opens another Pandora’s box of trouble. As in a lot of romantic comedies, the meet-cute in “Babygirl” has been strategically orchestrated. Romy is rushing to work on a day like any other when she’s stopped in her tracks by the sight of a dog ferociously attacking someone. Visibly shook, she continues to watch frozen as a tall, dark-haired, young stranger sharply commands the dog, which instantly stops its attack and nuzzles him. Romy is impressed, though not altogether for obvious reasons: In short order, it becomes clear that she too wants a firm hand, to nuzzle the commanding stranger and be commanded in turn.

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