With the increasing penetration of renewable energy, accurate and efficient probabilistic optimal power flow (POPF) calculation becomes more and more important to provide decision support for secure and economic operation of power systems. This paper develops a novel nonparametric probabilistic optimal power flow (N-POPF) model describing the probabilistic information by quantiles, which avoids any parametric probability distribution assumption of random variables. A novel critical region integral method (CRIM) combining multiparametric programming theory and discrete integral is proposed to efficiently solve the N-POPF problem. In the CRIM, the critical region partitioning algorithm is firstly introduced into the POPF model to directly establish the mapping relationship from wind power to optimal solutions of the POPF problem. Besides, a discrete integral method is developed in the CRIM to achieve the probability convolution calculation based on quantiles. Comprehensive numerical experiments verify the superior performance of the proposed CRIM in estimation accuracy and computational efficiency, and demonstrate that N-POPF model significantly improves the accuracy of uncertainty analysis. In general, the proposed method forms a new framework of POPF problem for power system analysis and operation.