This paper proposes an algorithm to calculate the optimal amplitude and phase of the harmonic current components that can be injected in the circulating currents of a modular multilevel converter (MMC) to minimize the capacitor voltage fluctuations. An optimal second harmonic component and an optimal set of second and fourth harmonic components are proposed. Simulation results are obtained in MATLAB/Simulink environment to study the effectiveness of the calculated optimal currents. Selected experimental results have been obtained from an MMC laboratory prototype, testing the effects of the circulating currents. The reported results demonstrate the effectiveness of using a fourth harmonic component in the circulating current, which improves the effect of the second harmonic on reducing the capacitor voltage fluctuations.