The problem of joint space-time decoding and multiple-access interference (MAI) rejection in multiple-access multiple-input multiple-output (MIMO) wireless communication systems is addressed. We assume that both the receiver and multiple transmitters are equipped with multiple antennas and that space-time block codes are used to send the data simultaneously from each transmitter to the receiver. A new linear minimum variance (MV) receiver structure is developed to decode the data sent from the transmitter-of-interest and to reject MAI, self-interference, and noise. Simulation results show that in multiple-access MIMO scenarios, the proposed receivers have a substantially lower symbol error rate as compared to the matched filter (MF) receiver which is equivalent to the maximum likelihood (ML) space-time decoder in the point-to-point MIMO communications case.