This work shows that a massive multiple-input multiple-output (MIMO) system with low-resolution analog-to-digital converters (ADCs) forms a natural extreme learning machine (ELM). The receive antennas at the base station serve as the hidden nodes of the ELM, and the low-resolution ADCs act as the ELM activation function. By adding random biases to the received signals and optimizing the ELM output weights, the system can effectively tackle hardware impairments, such as the nonlinearity of power amplifiers and the low-resolution ADCs. Moreover, the fast adaptive capability of ELM allows the design of an adaptive receiver to address time-varying effects of MIMO channels. Simulations demonstrate the promising performance of the ELM-based receiver compared to conventional receivers in dealing with hardware impairments.