This paper presents a new approach for guaranteed state estimation based on zonotopes for linear discrete-time multivariable systems with interval multiplicative uncertainties, in the presence of bounded state perturbations and noises. At each sample time, the presented approach computes a zonotope which contains the real system state. A P-radius-based criterion is minimized in order to decrease the size of the zonotope at each sample time and to obtain an increasingly accurate state estimation. The proposed approach allows one to efficiently handle the trade-off between the complexity of the computation and the accuracy of the estimation. An illustrative example is analyzed in order to highlight the advantages of the proposed state estimation technique.