In this work, we proposed and experimentally demonstrated a multiple-input multiple-output (MIMO) Volterra polynomial equalizer (MVPE), in a probabilistic shaping (PS) polarization-division multiplexed (PDM) 4096-quadrature amplitude modulation (QAM) coherent optical transmission system. In comparison with the conventional single-input single-output (SISO) Volterra nonlinear equalizers (VNLEs), the proposed MVPE can equalize the in-phase (I) and quadrature (Q) components in both the X and Y polarizations simultaneously and effectively alleviate nonlinear distortions. In the PS-PDM-4096-QAM experiment, the normalized generalized mutual information (NGMI) reached the threshold of DVB-S2 low-density parity-check (LDPC) codes with a 20% overhead. Compared to the SISO VNLE scheme, the MVPE scheme improves receiver sensitivity by approximately 2.8 dB while maintaining nearly similar computational complexity.