Massive multiple-input multiple-output (MIMO) systems employ a large number of antennas to achieve gains in capacity, spectral efficiency, and energy efficiency. However, the large antenna array also incurs substantial storage and computational costs. This paper proposes a novel data compression framework for massive MIMO channel matrices based on tensor Tucker decomposition. To address the substantial storage and computational burdens of massive MIMO systems, we formulate the high-dimensional channel matrices as tensors and propose a novel groupwise Tucker decomposition model. This model efficiently compresses the tensorial channel representations while reducing SINR estimation overhead. We develop an alternating update algorithm and HOSVD-based initialization to compute the core tensors and factor matrices. Extensive simulations demonstrate significant channel storage savings with minimal SINR approximation errors. By exploiting tensor techniques, our approach balances channel compression against SINR computation complexity, providing an efficient means to simultaneously address the storage and computational challenges of massive MIMO.