We study the influence of laser radiation on the electron transport through a molecular wire weakly coupled to two leads. In the absence of a generalized parity symmetry, the molecule rectifies the laser-induced current, resulting in directed electron transport without any applied voltage. We consider two generic ways of dynamical symmetry breaking: mixing of different harmonics of the laser field and molecules consisting of asymmetric groups. For the evaluation of the nonlinear current, a numerically efficient formalism is derived which is based upon the Floquet solutions of the driven molecule. This permits a treatment in the nonadiabatic regime and beyond linear response. (C) 2003 American Institute of Physics.