Context. Fairall 51 is a polar-scattered Seyfert 1 galaxy, a type of active galaxy believed to represent a bridge between unobscured type-1 and obscured type-2 objects. Fairall 51 has shown complex and variable X-ray absorption, but little is known about its origin. Aims. In our research, we observed Fairall 51 with the X-ray satellite Suzaku in order to constrain a characteristic time scale of its variability. Methods. We performed timing and spectral analysis of four observations separated by 1.5, 2, and 5.5 day intervals. Results. We found that the 0.5-50 keV broadband X-ray spectra are dominated by a primary power-law emission (with the photon index ∼2). This emission is affected by at least three absorbers with different ionisations (log ξ ≈ 1-4). The spectrum is shaped further by a reprocessed emission, possibly coming from two regions, the accretion disc and a more distant scattering region. The accretion disc emission is smeared by the relativistic effects, from which we measured the spin of the black hole as a ≈ 0.8 ± 0.2. We found that most of the spectral variability can be attributed to the least ionised absorber whose column density changed by a factor of two between the first (highest-flux) and the last (lowest-flux) observation. Conclusions. A week-long scale of the variability indicates that the absorber is located at the distance ≈0.05 pc from the centre, i.e., in the broad line region.