The optimization-based stabilization of manifolds for nonlinear dynamical systems with constraints is investigated. Manifolds in the state or output space are considered for which the original system description can be transformed into a so-called transverse normal form. With this formulation, the motion of the system transverse and tangential to the manifold can be separately described. The transverse normal form is combined with a tailored model predictive control scheme to achieve the objectives of stabilizing the manifold, rendering it invariant, and imposing a desired motion on the manifold under due consideration of constraints. Furthermore, the stabilization of the manifold is prioritized over the movement on the manifold. Convergence of the model predictive control scheme is proven. The applicability of the proposed concept is demonstrated by an illustrative simulation example. (C) 2016 Elsevier Ltd. All rights reserved.