For high-speed packet access, hybrid automatic repeat request (HARQ) and multiple-input multiple-output (MIMO) multiplexing are indispensable techniques. As the multiple-access technique, single carrier (SC)-frequency-division multiple-access (FDMA) using transmit filtering is promising. The use of square-root Nyquist transmit filter reduces peak-to-average power ratio (PAPR) of the transmit SC-FDMA signal and increases the frequency diversity gain. However, if the carrier-frequency separation among multiple-access users is kept the same as in the case of the transmit filter's roll-off factor alpha=0 (i.e., brick wall filter), the adjacent users' signal spectra overlap and the multi-user interference (MUI) is produced. In this paper, we propose an iterative minimum mean square error signal detection and interference cancellation (MMSED-IC) for turbo coded uplink SC-FDMA MIMO using HARQ. In the proposed MMSED-IC, not only the inter-antenna interference (IAI) and residual inter-symbol interference (ISI) but also MUI are cancelled in an iterative fashion. We evaluate the HARQ throughput performances by computer simulation, and show that by using the proposed scheme, SC-FDMA with alpha=1 can achieve higher throughput performance than not only SC-FDMA with alpha=0 but also OFDMA using IAI cancellation.