Nuclear effective field theory (NEFT) including pions in the two-nucleon sector is examined from the Wilsonian renormalization group point of view. The pion exchange is cut off at the floating cutoff scale, Λ, with the short-distance part being represented as contact interactions in accordance with the general principle of renormalization. We derive the nonperturbative renormalization group equations in the leading order of the nonrelativistic approximation in the operator space up to including O(p2), and find the nontrivial fixed points in the 1S0 and 3S1-3D1 channels which are identified with those in the pionless NEFT. The scaling dimensions, which determine the power counting, of the contact interactions at the nontrivial fixed points are also identified with those in the pionless NEFT. We emphasize the importance of the separation of the pion exchange into the short-distance and the long-distance parts, since a part of the former is nonperturbative while the latter is perturbative. © 2011 American Physical Society.