In this paper we consider a Stokes system with Navier-slip boundary conditions. The main results concern the behavior of the cost of null controllability with respect to the diffusion coefficient when the control acts in the interior. In particular, we prove in (0, pi)(2) that for a sufficiently large time the cost decays exponentially as the diffusion coefficient vanishes, whereas in (0, pi)(3) we prove that for most of the control domains and for any time T > 0 the cost explodes exponentially as the diffusion coefficient vanishes.