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We present a complete X-ray spectral analysis of the obscured AGN in NGC 4945, based on a Suzaku campaign spanning a period of seven months. NGC 4945 is the archetypal Compton-thick Seyfert 2 galaxy, with a reflection-dominated spectrum below 10 keV, and the intrinsic emission visible only at higher energies. Taking advantage of the unique Suzaku-HXD capabilities we detect for the first time absorption variations larger than 1024 cm−2 on time scales of a few weeks, suggesting that the obscuring material consists of gas clouds at parsec-scale distance. This result proves the fundamental importance of a time-resolved broadband X-ray study of AGNs.