Based on thorough analyses of adverse effects from nonlinear distortion caused by high power amplifiers (HPAs) with phase conversion in multiple-input multiple-output space-time block code (MIMO-STBC) systems, this work proposes a nonparametric phase estimation and compensation method for the received signal. Using the optimal feedforward blind estimation technique, the receive signal's rotated phase is estimated and efficiently compensated, allowing to considerably eliminate the detrimental effect of phase distortion without any tradeoff of transmission rate. Numerical simulations verify the relevance of theoretical arguments and efficiency of the proposed compensation scheme.