Low complexity approximate message passing (AMP) orthogonal frequency division multiplexing combined with index modulation (OFDM-IM) detection algorithms are proposed, which exploit the sparse structure of the frequency domain (FD) OFDM-IM symbols. To circumvent the high root mean square error (RMSE) in the conventional AMP algorithm, a minimum mean square error (MMSE) denoiser is proposed based on the classic Bayesian approach and on the state evolution of AMP. Our simulation results demonstrate that it is capable of improving both the RMSE as well as the convergence rate. However, in practice, the channel's diagonal FD matrix may be a non-Gaussian sensing matrix, hence a damping strategy is conceived. In conclusion, the proposed MMSE denoiser based damping-assisted AMP-aided detector strikes a compelling bit error ratio vs. complexity trade-off.