The robust reduced order observer for a class of discrete-time Lipschitz nonlinear systems with external disturbance is proposed. It is shown that the proposed observer design can suppress the effect on the estimation error of external disturbance up to the prescribed level. Also, linear matrix inequalities are used to represent sufficient conditions on the existence of the proposed observer. Moreover, the maximum admissible Lipschitz constant of the proposed design is obtained for a given disturbance attenuation level. Finally, an illustrative example is given to verify the effectiveness of the proposed design.