Massive multiple-input multiple-output (mMIMO) systems and filtered multi-carrier waveforms have recently emerged as hot research topics in next-generation wireless networks. This paper extends the use of Overlap-Save Filter Bank Multi-Carrier (FBMC) receivers to mMIMO communication systems and investigates the corresponding FBMC transceiver advantages over OFDM. To this aim, we derived the signal-to-interference ratio (SIR) expressions analytically under several channel impairments such as timing offsets and carrier frequency offsets. Furthermore, we conducted an asymptotic study on the performance of FBMC augmented with our proposed receivers in the context of massive MIMO systems. While still outperforming OFDM, results for FBMC show that increasing the number of base station (BS) antennas does not increase the SINR unboundedly. We have validated the proposed analytical study by comparing its results with those obtained from Monte Carlo simulations and confirmed the superiority of the proposed receivers over those in mMIMO literature. Moreover, analytical and simulation results confirm that the Overlap-Save FBMC receiver can support asynchronous communications in the context of mMIMO, a cornerstone for grant-free communications and massive access.