This paper considers the multiple-input multiple-output (MIMO) system with linear minimum mean square error (MMSE) detection under ideal fast fading. For $N_t$ transmit and $N_r({geq}N_t)$ receive antennas, we derive the achievable ergodic capacity of MMSE detection exactly. When MMSE detection is considered in a receiver, we introduce a different approach that gives the approximation of a MIMO channel capacity at high signal-to-noise ratio (SNR). The difference between the channel capacity and the achievable capacity of MMSE detection converges to some constant that depends only on the number of antennas. We validate the analytical results by comparing them with Monte Carlo simulated results.