Reprimanded for wearing her headscarf too loosely, Shideh, a former medical student in Tehran, is warned: “A woman should be more scared of exposing herself than anything else.”

Shideh has other concerns. It is 1988, the height of the Iran-Iraq war, and her husband is on the frontline, leaving her to raise their seven-year-old daughter. Shideh’s ambitions to become a doctor have been torpedoed by accusations of political activity during the Iranian revolution. There are also regular air raids to contend with. Scarier than any bomb, though, is the prospect that a djinn – a malevolent spirit – may be preying on her family.

Based on Babak Anvari’s 2016 film, Carmen Nasr’s taut adaptation could scarcely be timelier. When Shideh and her neighbours huddle together in their bomb shelter, cursing Europe and the US for abandoning them, this could be a livestream from 2026.

But the strength of Nadia Latif’s suspenseful, fluidly directed production lies in its interlocking relationship between action and metaphor. Even as we interpret the djinn as a manifestation of Shideh’s internalised anger from her lifetime of oppression, that doesn’t make it any less terrifying – as proved by the nerve-shredding jumpscare at the end of act one.

The stage is dominated by Ben Stones’s lovingly detailed set: a widescreen living room with mustard-yellow walls, cosily cluttered furniture and unreachable recesses, with a TV in the corner playing Jane Fonda workout tapes on a contraband VCR. Donato Wharton’s sound design, with its scorched electronic edge, ratchets up the tension, while James Farncombe’s lighting helps delineate the bomb shelter, a sunken space in front of the stage, and feeds the air of melancholy as well as menace.

Relationships between Shideh’s neighbours, be they fragile or belligerent (“Let’s stay to spite Saddam!” says one), provide the drama’s foundation. Leila Farzad naturally makes the strongest impression, her frazzled tenacity as Shideh driving the action. There is real delicacy, too, in her mapping of Shideh’s damaged interior landscape. In her impressive final scenes, a new sort of self-exposure is required, nothing to do with headscarves but built of an emotional transparency between mother and daughter that leaves them forearmed for future battles.

• At the Almeida theatre, London, until 4 July