Electromagnetic response of a finite-width two-dimensional electron stripe is theoretically studied. It is shown that retardation and radiative effects substantially modify the absorption spectrum of the system at microwave frequencies, leading to a nontrivial zigzag behavior of the magnetoplasmon-polariton modes in magnetic fields, similar to that recently observed by Kukushkin [Phys. Rev. Lett. 90, 156801 (2003)].