In this paper it is proved that wave maps can be obtained by a penalization method using certain regularity conditions on the initial data, otherwise the solutions of the penalized equation converge weakly to a solution of the system of coupled equations obtained by Keller and Rubinstein by a multi-scale formal analysis. In particular, the interaction of the rapid normal oscillations and the tangential motions creates a new (hyperbolic) term in the limit system whose well-posedness is proved by using the Nash-Moser implicit function theorem.