Accurate channel state information (CSI) prediction is crucial for next-generation multiple-input multiple-output (MIMO) communication systems. Classical prediction methods often become inefficient for high-dimensional and rapidly time-varying channels. To improve prediction efficiency, it is essential to exploit the inherent low-rank tensor structure of the MIMO channel. Motivated by this observation, we propose a dynamic mode decomposition (DMD)-based prediction framework operating on the low-dimensional core tensors obtained via a Tucker decomposition. The proposed method predicts reduced-order channel cores, significantly lowering computational complexity. Simulation results demonstrate that the proposed approach preserves the dominant channel dynamics and achieves high prediction accuracy.