Context. Despite the low elemental deuterium abundance in the Galaxy, enhanced molecular deuterium fractionation has been found in the environments of low-mass star-forming regions and, in particular, the Class 0 protostar IRAS 16293-2422. Aims. The key program Chemical HErschel Surveys of Star forming regions (CHESS) aims at studying the molecular complexity of the interstellar medium. The high sensitivity and spectral resolution of the Herschel/HIFI (Heterodyne Instrument for Far-Infrared) instrument provide a unique opportunity to observe the fundamental 1_1,1-0_0,0 transition of ortho-D₂O at 607 GHz and the higher energy 2_1,2-1 _0,1 transition of para-D₂O at 898 GHz, both of which are inaccessible from the ground. Methods. The ortho-D₂O transition at 607 GHz was previously detected. We present in this paper the first tentative detection for the para-D₂O transition at 898 GHz. The spherical Monte Carlo radiative transfer code RATRAN was used to reproduce the observed line profiles of D₂O with the same method that was used to reproduce the HDO and H₂¹⁸O line profiles in IRAS 16293-2422. Results. As for HDO, the absorption component seen on the D₂O lines can only be reproduced by adding an external absorbing layer, possibly created by the photodesorption of the ices at the edges of the molecular cloud. The D ₂O column density is found to be about 2.5 × 10¹² cm^-2 in this added layer, leading to a D₂O/H₂O ratio of about 0.5%. At a 3σ uncertainty, upper limits of 0.03% and 0.2% are obtained for this ratio in the hot corino and the colder envelope of IRAS 16293-2422, respectively. Conclusions. The deuterium fractionation derived in our study suggests that the ices present in IRAS 16293-2422 formed on warm dust grains (~15-20 K) in dense (~10⁴-5 × 10⁴ cm ^-3) translucent clouds. These results allow us to address the earliest phases of star formation and the conditions in which ices form.