A filter is required to eliminate the high-frequency switching ripple present in the input current of a matrix converter (MC). Design of such a filter requires an estimation of the higher harmonic components present in the input current. This paper presents a simple closed-form analytical expression for the RMS input current ripple injected by the MC. The expression shows the variation with load power factor and is independent of the output frequency. This is used in a step-by-step procedure to design various input filter components from the specifications of allowable total harmonic distortion in the grid current and distortion in the input voltage. The MC is modeled for the grid frequency component in order to evaluate the design for input power factor and voltage drop across the filter. A damping resistance has been designed ensuring minimum ohmic loss. The analytical estimation of the ripple current and the proposed design procedure have been validated by simulations in MATLAB/Simulink and experiments on a laboratory prototype.