In this letter, a low-complexity approximation for instantaneous mutual information (IMI) of spatial modulation multiple-input single-output systems is presented. Based on this low-complexity approximation, a closed-form approximation for the average mutual information (MI) is derived. The approximation closely follows exact average MI values for different numbers of antennas and a wide range of signal-to-noise ratios. The proposed approximation for the IMI has a considerably lower computational complexity compared to previously proposed bounds. Also, the closed-form approximation of the average MI is considerably less complex than previously proposed bounds that require numerical averaging over randomly generated channel realizations.