Automatic modulation classification (AMC) plays a vital role in cognitive radio to improve spectrum utilization efficiency, however, most of the existing works have focused on single-carrier communications in single-input single-output systems. In this paper, we propose an efficient AMC method for multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) communication systems with the assumption of unknown frequency-selective fading channels and signal-to-noise ratio. At the receiver, the complex envelope samples of a burst signal acquired by multiple antennas are decomposed into in-phase and quadrature samples, which are then structured into a high-dimensional data array. To learn the modulation patterns from received signals, we develop a deep network, namely three-dimensional MIMO-OFDM convolutional neural network (MONet). With cuboidal convolution filters, the proposed MONet allows the network to capture underlying features as intra- and inter-antenna correlations at multi-scale signal representations. Relying on simulations, MONet achieves the classification accuracy of over 95% at 0 dB SNR under various channel impairments and shows the robustness with different MIMO antenna configurations.