The geometric spin Hall effect of light (GSHEL), similar to the spin Hall effect of light, is also a spin-dependent shift in the centroid of light intensity (energy flux), but it is a purely geometric effect and independent of the light-matter interaction. In this paper, we discuss the GSHEL with respect to momentum flux instead of energy flux. Interestingly, for the symmetric energy-momentum (E-M) tensor, its centroid shift of momentum flux is double that of the energy flux; however, for the canonical E-M tensor, its centroid shift of momentum flux agrees with that of the energy flux. Furthermore, when considering the effect produced by orbital angular momentum, for these two conventional E-M tensors the centroid shifts of the momentum fluxes are twice those of the energy fluxes. To tell which E-M tensor of the electromagnetic field would be more "correct," we propose a possible experimental scheme to test the GSHEL of momentum flux through the mechanical effect of light.