In the recent literature there is circumstantial evidence that the viscosity of the intracluster medium may not be too far from the Spitzer value. In this letter, we present two-dimensional hydrodynamical simulations of ram pressure stripping of disc galaxies in a viscous intracluster medium. The values of viscosity explored range between 0.1 and 1.0 times the Spitzer value. We find that viscosity affects the appearance and the dimensions of the galactic wakes but has very little effect on the evolution of the gas mass of the galaxy.