We investigated effects of hydrodynamic interactions on diffusivities of proteins that undergo rotation-coupled sliding along DNA. For that, we applied numerical calculations of mobility and friction tensors to systems consisting detailed bead-shell models of DNA and proteins of different size. Using tensors that result from these calculations along with an expression for the instantaneous energy dissipation rate due to motions of a nonspecifically bound protein that follows a helical track around DNA, we evaluated apparent one-dimensional friction and mobility coefficients for model proteins. The results that we obtained indicate that hydrodynamic interactions between DNA and proteins may substantially (even several-fold) reduce the apparent one-dimensional diffusivity of proteins, when compared with results of other theoretical analyses of the rotation-coupled sliding of proteins along DNA that neglect hydrodynamic effects. Moreover, accounting for hydrodynamic effects decreases the gap between values of diffusion coefficients of proteins on DNA measured experimentally and those estimated based on theoretical calculations and analyses applied to model systems. Altogether, the current study gives insights into the significance of hydrodynamic interactions in determination of the rate of finding target sites by DNA-binding proteins.