Dynamic shaking imposed by passing seismic waves is able to promote various hydrological processes in fractured reservoirs. This is often associated with seismically‐induced fracture unclogging due to mobilization of deposited colloids in the fracture network which, in turn, affects permeability at the reservoir scale. Numerous laboratory and field studies pointed out that fracture unclogging can be initiated when viscous shear stresses in the fracture fluid are in the range of 0.1‐1 Pascals. In this numerical study, we compute viscous shear stress in a fluid‐saturated fractured medium due to the action of passing P‐ and S‐waves. We perform a sensitivity analysis in terms of fluid, fracture, and host rock physical properties as well as seismic wave characteristics. Our results show that seismically‐induced viscous shearing increases with frequency and seismic strain and can be in the order of those initiating fracture unclogging for typical seismic strains and frequencies. S‐waves tend to produce viscous shearing approximately two times larger than P‐waves and, for anisotropic distribution of fractures, it is extremely dependent on the direction of wave propagation. Moreover, larger viscous shearing is expected for more viscous fluids and stiffer host rocks. Regarding the fracture network distribution, for the same fracture density, the presence of longer fractures drastically increases the potential of fracture unclogging at seismic frequencies. The fracture aperture distribution, on the other hand, can also affect the development of viscous shearing. Fractures with correlated distributions of contact areas exhibit an order of magnitude larger viscous shearing than uncorrelated ones.