Although the multi-antenna or so-called multiple-input multiple-output (MIMO) transmission has been the enabling technology for the past generations of radio-frequency (RF)-based wireless communication systems, its application to the visible light communication (VLC) still faces a critical challenge as the MIMO spatial multiplexing gain can be hardly attained in VLC channels due to their strong spatial correlation. In this paper, we tackle this problem by deploying the optical intelligent reflecting surface (OIRS) in the environment to boost the capacity of MIMO VLC. Firstly, based on the extremely near-field channel condition in VLC, we propose a new channel model for OIRS-assisted MIMO VLC and reveal its peculiar ``no crosstalk'' property, where the OIRS reflecting elements can be respectively configured to align with one pair of transmitter and receiver antennas without causing crosstalk to each other. Next, we characterize the OIRS-assisted MIMO VLC capacities under different practical power constraints and then proceed to maximize them by jointly optimizing the OIRS element alignment and transmitter emission power. In particular, for optimizing the OIRS element alignment, we propose two algorithms, namely, location-aided interior-point algorithm and log-det-based alternating optimization algorithm, to balance the performance versus complexity trade-off; while the optimal transmitter emission power is derived in closed form. Numerical results are provided, which validate the capacity improvement of OIRS-assisted MIMO VLC against the VLC without OIRS and demonstrate the superior performance of the proposed algorithms compared to baseline schemes.