We study the robust or H-infinity exponential stabilization of the linearized Navier-Stokes equations around an unstable stationary solution in a two-dimensional domain Omega. The disturbance is an unknown perturbation in the boundary condition of the fluid flow. We determine a feedback boundary control law, robust with respect to boundary perturbations, by solving a max-min linear quadratic control problem. Next we show that this feedback law locally stabilizes the Navier-Stokes system. Similar problems have been studied in the literature in the case of distributed controls and disturbances. To the authors' knowledge, it is the first time that the robust stabilization of the Navier-Stokes equations is studied for boundary controls and boundary disturbances.