Automatic modulation recognition is the core algorithm in the field of modulation classification in communication systems. Our investigations show that deep learning (DL) based modulation recognition techniques have achieved effective progress for multiple-input multiple-output (MIMO) systems. However, network complexity is always an additional burden for high-accuracy classifications, which makes it impractical. Therefore, in this paper, we propose a low-complexity dimensional interactive lightweight network (DilNet) for MIMO systems. Specifically, the signals received by different antennas are cooperatively input into the network, and the network calculation amount is reduced through the depth-wise separable convolution. A two-dimensional interactive attention (TDIA) module is designed to extract interactive information of different dimensions, and improve the effectiveness of the cooperation features. In addition, the TDIA module ensures low complexity through compressing the convolution dimension, and the computational burden after inserting TDIA is also acceptable. Finally, the network is trained with a penalized statistical entropy loss function. Simulation results show that compared to existing modulation recognition methods, the proposed DilNet dramatically reduces the model complexity. The dimensional interactive lightweight network trained by penalized statistical entropy also performs better for recognition accuracy in MIMO systems.