We report the results from a 2011 Suzaku observation of the nearby low-ionization BAL quasar/ULIRG Markarian 231. These data reveal that the X-ray spectrum has undergone a large variation from the 2001 XMM-Newton and BeppoSAX observations. We interpret this finding according to a scenario whereby the X-ray continuum source is obscured by a two-component partial-covering absorber with NH ~10^22 and ~10^24 cm^-2, respectively. The observed spectral change is mostly explained by a progressive appearance of the primary continuum at <10 keV due to the decrease of the covering fraction of the denser absorption component. The properties of the X-ray obscuration in Mrk 231 match well with those of the X-ray shielding gas predicted by the theoretical models for an efficient radiatively-driven acceleration of the BAL wind. In particular, the X-ray absorber might be located at the extreme base of the outflow. We measure a 2-10 keV luminosity of L(2-10) = 3.3 x 10^43 erg s^-1 for the 2011 data set, i.e. an increase of 30% with respect to the 2001 value.