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Wireless communication systems working in millimeter-wave (mmWave) frequency bands offer higher bandwidths than traditional radio frequency schemes. This technology allows multibeam steering and data multiplexing with the help of massive multiple-input multiple-output (MIMO) systems. However, supporting large bandwidths at mmWave frequencies is challenging due to the use of large antenna arrays with beamforming, sampling signals with large bandwidths, and baseband signal processing operations at gigabit data rates. Due to the wider bandwidth and higher signal processing requirements of mmWave systems, low-complexity receiver algorithms become important. Previously reported investigations assumed the use of hybrid beamforming structures that reduce power consumption and signal processing tasks. Therefore, the use of artificial neural networks (ANNs) becomes relevant for the processing of mmWave signals as reported in earlier works. In this article, to carry out MIMO combining processing for mmWave communications, we propose a fully complex multilayer extreme learning machine (M-ELM) neural network. We investigate the tuning of the number of neurons in each hidden layer for the proposed method to maximize the system performance and decrease the complexity of the receiver. We compare the results of the introduced M-ELM algorithm with a fully complex extreme learning machine (ELM), fully real ELM, and M-ELM defined in the real plane in terms of spectral efficiency, bit error rate, computational complexity, and processing time. Furthermore, we compare the novel M-ELM strategy with traditional linear MIMO receivers, such as Maximum Ratio and Minimum Mean Square Error, as well as to a multilayer perceptron (MLP) neural network trained offline. The numerical results show that with a good balance between the overall performance and computational cost of the ANN, the fully complex M-ELM MIMO receiver outperforms the other evaluated schemes.