The nonlinear magneto-optical Ken-effect (NO-LIMOKE) is determined for freestanding Fe monolayers with several in-plane structures from first principles. Based on the theory of nonlinear magneto-optics by Hubner and Bennemann [1] we calculate the nonlinear susceptibilities of the monolayers using the ab initio FLAPW-method WIEN95 with the additional implementation of spin-orbit coupling and the calculation of the dipole transition matrix elements appropriate for freestanding monolayers. We present results for the spectral dependence of the nonlinear susceptibility tensor elements and the resulting intensities and Ken angles. Special emphasis is put on the effects of structural changes, such as the variation of the lattice constant and different surface orientations. The influence of spin-orbit coupling on the tensor elements for different magnetization directions is presented. Also, the azimuthal dependence of the intensities generated by several low-index surfaces is given, showing the pronounced sensitivity of second-harmonic generation to lateral structural changes and magnetic properties even in the monolayer range.