Context: Despite the low elemental deuterium abundance in the Galaxy, enhanced molecular D/H ratios have 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 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 H2-18O 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 D2O column density is found to be about 2.5e12 cm^{-2} in this added layer, leading to a D2O/H2O ratio of about 0.5%. At a 3 sigma 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 (~1e4-5e4 cm^{-3}) translucent clouds. These results allow us to address the earliest phases of star formation and the conditions in which ices form.