We study the possibility of removing the cyclic prefix (CP) overhead from orthogonal frequency division multiplexing (OFDM) in massive multiple-input multiple-output (MIMO) systems. We consider the uplink transmission, while our results are applicable to the downlink as well. The absence of CP increases the spectral efficiency in expense of intersymbol interference and intercarrier interference. It is known that in massive MIMO, the effects of uncorrelated noise and multiuser interference vanish as the number of base station antennas tends to infinity. To investigate if the channel distortions in the absence of CP fade away, we study the performance of the standard maximum ratio combining receiver. Our analysis reveals that in this receiver, there always remains some residual interference leading to saturation of signal-to-interference-plus-noise ratio. To resolve this problem, we propose using the time reversal (TR) technique. Moreover, in order to further reduce the multiuser interference, we propose a zero-forcing equalization to be deployed after the TR combining. We compare the achievable rate of the proposed system with that of the conventional CP-OFDM. We show that in realistic channels, a higher spectral efficiency is achieved by removing the CP from OFDM, while reducing the computational complexity.