We present IRAM 30 m and JCMT observations of HDO lines towards the solar-type protostar IRAS 16293-2422. Five HDO transitions have been detected on-source, and two were unfruitfully searched for towards a bright spot of the outflow of IRAS 16293-2422. We interpret the data by means of the Ceccarelli et al. (1996) model, and derive the HDO abundance in the warm inner and cold outer parts of the envelope. The emission is well explained by a jump model, with an inner abundance x_in ^HDO = 1 × 10^-7 and an outer abundance x_out ^HDO ≤ 1 × 10^-9 (3σ). This result is in favor of HDO enhancement due to ice evaporation from the grains in the inner envelope. The deuteration ratio HDO/H₂O is found to be f_in = 3% and f_out ≤ 0.2% (3σ) in the inner and outer envelope respectively and therefore, the fractionation also undergoes a jump in the inner part of the envelope. These results are consistent with the formation of water in the gas phase during the cold prestellar core phase and storage of the molecules on the grains, but do not explain why observations of H₂O ices consistently derive a H₂O ice abundance of several 10^-5 to 10^-4, some two orders of magnitude larger than the gas phase abundance of water in the hot core around IRAS 16293-2422.