We have obtained the first accurate determination of the albedo of (99942) Apophis, by means of polarimetric observations carried out at the VLT. The observations allowed us to obtain the slope of the polarization–phase curve of this object, from which an albedo estimate of 0.33 ± 0.04 could be obtained. From our observations we also obtained a new estimate of the absolute magnitude: H = 19.7 ± 0.2 (assuming G=0.25, which applies to S- and Q-type asteroids). Based on these results, we derive for the size of Apophis a value of 270 ± 30 meters. The accuracy of this size estimate is mostly related to uncertainties in H, whereas the obtained albedo value should be considered more robust. Our observations convincingly show that polarimetry is an effective and efficient tool to obtain accurate albedos and sizes for small and faint potentially hazardous asteroids.