In this paper, a pair of novel frequency domain equalizers for broadband single-carrier (SC) spatial modulation (SM) systems over dispersive channels are proposed by integrating with the concept of generalized approximate message passing (GAMP). Specifically, we first propose a GAMP-aided frequency domain turbo equalizer (FDTE-GAMP) operating on a vector-by-vector basis, which exploits the linear mixing channel structure composed of channel matrix and fast Fourier transforms. In the design of this novel detector, the non-Gaussian property of the transmitted SM symbol is fully investigated, in order to provide a more reliable belief of the channel symbols, leading to an accurate extrinsic information. For the sake of simplification, we propose a low-complexity version of FDTE-GAMP by forcing the variance components of transmitted symbols to be the same scalar, and thus avoiding the matrix inversion operation and maintaining a sequence of scalar operations. Simulation results show that the proposed equalizers are capable of providing a better tradeoff between the attainable bit error rate and the imposed computational complexity than the conventional FDTEs conceived for SC-SM systems.