We present a time, spectral and imaging analysis of the X-ray reflector in NGC 4945, which reveals its geometrical and physical structure with unprecedented detail. NGC 4945 hosts one of the brightest AGN in the sky above 10 keV, but it is only visible through its reflected/scattered emission below 10 keV, due to absorption by a column density of ∼4 × 1024 cm−2. A new Suzaku campaign of five observations spanning ∼6 months, together with past XMM–Newton and Chandra observations, shows a remarkable constancy (within <10 per cent) of the reflected component. Instead, Swift-BAT reveals strong intrinsic variability on time-scales longer than 1 yr. Modelling the circumnuclear gas as a thin cylinder with the axis on the plane of the sky, we show that the reflector is at a distance ≥30–50 pc, well within the imaging capabilities of Chandra at the distance of NGC 4945 (1 arcsec ∼18 pc). Accordingly, the Chandra imaging reveals a resolved, flattened, ∼150 pc long clumpy structure, whose spectrum is fully due to cold reflection of the primary AGN emission. The clumpiness may explain the small covering factor derived from the spectral and variability properties.