This paper proposes an approach to deal with the problem of robust output feedback model predictive control for linear discrete-time systems subject to state and input constraints , in the presence of unknown but bounded disturbances and measurement noises. The estimation of the states is built using a zonotopic set-membership estimation. This set is time-decreasing and is computed off-line as the solution of a Linear Matrix Inequality optimization problem. The control law is designed by using tube-based model predictive control such that the closed-loop stability is guaranteed and the state and input constraints are fulfilled. The proposed methodology is illustrated through numerical simulations.