Multiple-input multiple-output orthogonal frequency division multiplexing with index modulation (MIMO-OFDM-IM) is a relatively new multicarrier transmission technique for the MIMO systems to achieve both energy and spectral efficiency. However, due to the dependence of subcarrier symbols introduced by the index modulation, existing MIMO detection techniques cannot be applied in MIMO-OFDM-IM as it will lead to erroneous detection on index information of the active subcarriers and further deteriorate the system performance. In this paper, we first develop an optimal detection algorithm with reduced complexity for MIMO-OFDM-IM by performing the subcarrier-wise detection under the constraint on the legal subcarrier combination within each OFDM-IM subblock. To further reduce the computational complexity, we then propose a low-complexity subcarrier-wise algorithm based on the deterministic sequential Monte Carlo technique to achieve near-optimal detection for MIMO-OFDM-IM. Specifically, the near-optimal detector applies the QR decomposition to generate an upper triangular structure and draw antenna-wise samples at the subcarrier level. Computational simulations and complexity analysis show that the proposed algorithms provide similar performance to optimal one with reduced computational complexity.