In conventional multicarrier systems, a cyclic prefix (CP) is added to the transmission block in order to protect it from multi-path propagation of the wireless channel. Nonetheless, due to the random nature of the CP, it is usually discarded at the receiver side, and from a synchronization perspective, this energy is wasted. Unique Word (UW) is a promising concept for CP replacement, because, in addition to protecting the signal from multi-path propagation, it allows per-block synchronization. Considering a multiple-input-multiple-output (MIMO) system, the state-of-the-art (SoA) data-aided synchronization approaches are mainly preamble based, while, on the other hand, the synchronization techniques for UW sequences are being applied to single-input-single-output systems in low mobility scenarios. In this paper, we investigate time and frequency synchronization of UW-based MIMO systems in high mobility conditions where the wireless channel is both frequency selective and fast fading. Through theoretical derivations as well as extensive simulations, we show that the proposed UW-based synchronization approach for MIMO outperforms the SoA MIMO synchronization techniques.