In this paper we deal with the local exact controllability of theNavier-Stokes system with nonlinear Navier-slip boundaryconditions and distributed controls supported in small sets. In afirst step, we prove a Carleman inequality for the linearizedNavier-Stokes system, which leads to null controllability of thissystem at any time T>0. Then, fixed point arguments lead to thededuction of a local result concerning the exact controllabilityto the trajectories of the Navier-Stokes system.