As shown by Wrobel, Mishuris, and Piccolroaz (2017), the hydraulically induced tangential traction on fracture walls changes local displacement and stress fields. This resulted in the formulation of a new hydraulic fracture (HF) propagation condition based on the critical value of the energy release rate that accounts for the hydraulically-induced shear stress. Therefore it is clear that the crack direction criteria, which depend on the tip distributions of the stress and strain fields, need to be changed. We analyse the two commonly used criteria, one based on the maximum circumferential stress (MCS) and another - on the minimum strain energy density (MSED). We show that the impact of the hydraulically induced shear stress on the direction of the crack propagation is negligible in the case of large material resistance to fracture, while for small toughness the effect is significant. Moreover, values of the redirection angles, corresponding to the so-called viscosity dominated regime (KIC → 0), depend dramatically on the ratios of the stress intensity factors.