The application of multiple-input multiple-output (MIMO) technique to sparse code multiple access (SCMA) systems is important to enhance the system performance of future fifth generation wireless networks. However, one of the challenges in design of downlink MIMO-SCMA systems is developing near-optimum bit error rate (BER) performance detectors with affordable computational costs. To achieve this goal, we construct a joint sparse graph combining the single graph of MIMO channels and SCMA codewords, and then design the corresponding virtual SCMA codebooks for the detector. To utilize them, a novel joint processing approach based on message passing algorithm is proposed. Furthermore, two strategies for message update on the joint sparse graph, i.e., parallel and serial schedules, are, respectively, presented. Simulations show that, the proposed detector can achieve the optimal BER performance with significantly reduced complexity, compared to the maximum likelihood detector.