Faster-than-Nyquist (FTN) signaling is investigated for quasi-static flat fading massive multiple-input multiple-output (MIMO) systems. In FTN signaling, pulse trains are sent at a symbol rate higher than the Nyquist rate to increase the transmission rate. As a result, inter-symbol interference occurs inevitably for flat fading channels. This paper assesses the information-theoretically achievable rate of MIMO FTN signaling based on the optimum joint equalization and multiuser detection. The replica method developed in statistical physics is used to evaluate the achievable rate in the large-system limit, where the dimensions of input and output signals tend to infinity at the same rate. An analytical expression of the achievable rate is derived for general modulation schemes in the large-system limit. It is shown that FTN signaling does not improve the channel capacity of massive MIMO systems, and that FTN signaling with quadrature phase-shift keying achieves the channel capacity for all signal-to-noise ratios as the symbol period tends to zero.