This paper analyzes the output signal-to-interference-plus-noise ratio (SINR) for a multiple-input multiple-output (MIMO) multicarrier code division multiple access (MC-CDMA) system with minimum mean square error receivers. Previous work on a single antenna MC-CDMA system is based on convergence of the limiting spectral distribution of large dimensional sample covariance matrices and the asymptotic freeness between random matrices. These concepts cannot directly be applied to a MIMO MC-CDMA system because some assumptions for single antenna do not match the case of multiple antenna. Therefore, this paper expands the concept of convergence and freeness to MIMO system by using extended Haar unitary random matrix and the Marcěnko-Pastur law. The analysis shows that the output SINR asymptotically converges to a deterministic value with a closed form expression. The analysis is used to obtain improved bit error rate calculation as verified by simulations.