This article presents an Index modulated MIMO-GFDM system. In addition to the diversity/multiplexing gains and appealing spectral characteristics typical of MIMO-GFDM systems, the use of index modulation (IM) applied to the subcarriers within a GFDM block results in attractive characteristics to the system, in terms of the spectral efficiency, detection performance and computational complexity. Two detection strategies for IM-MIMO-GFDM are presented, offering different detection performance and computation complexity balances. Ultimately, the computational results obtained offer a significant insight into the choice of the values of the index modulation block parameters in terms of achieving a favorable spectral efficiency/BER/computational complexity balance.