This paper presents a novel online model predictive control framework based on automatic time warping. In general, existing model predictive control frameworks employ reference motions with sampling time uniform and fixed. Unlike these, our framework allows to change the sampling time of a reference motion based on physics-based simulation so that the character effectively responds to external forces unexpectedly applied to it. In order to do so, we formulate an optimal control problem, taking into account both optimal time warping and full-body dynamics simultaneously. We adopt differential dynamic programming to produce an optimal control policy by solving the problem, which is used to compute the optimal feedback information for character motion and sampling time. We show the robustness of our framework to external perturbations through experiments. We also show the effectiveness of this framework for rhythmic motion synthesis.