Reservoir computing (RC) is a class of neuromorphic computing approaches that deals particularly well with time-series prediction tasks. It significantly reduces the training complexity of recurrent neural networks and is also suitable for hardware implementation whereby device physics are utilized in performing data processing. In this paper, the RC concept is applied to detecting a transmitted symbol in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Due to wireless propagation, the transmitted signal may undergo severe distortion before reaching the receiver. The nonlinear distortion introduced by the power amplifier at the transmitter may further complicate this process. Therefore, an efficient symbol detection strategy becomes critical. The conventional approach for symbol detection at the receiver requires accurate channel estimation of the underlying MIMO-OFDM system. However, in this paper, we introduce a novel symbol detection scheme where the estimation of the MIMO-OFDM channel becomes unnecessary. The introduced scheme utilizes an echo state network (ESN), which is a special class of RC. The ESN acts as a black box for system modeling purposes and can predict nonlinear dynamic systems in an efficient way. Simulation results for the uncoded bit error rate of nonlinear MIMO-OFDM systems show that the introduced scheme outperforms conventional symbol detection methods.