Transmission of microwave spin waves through a microstructured magnonic crystal in the form of a Permalloy waveguide of a periodically varying width was studied experimentally and theoretically. The spin wave characteristics were measured by spatially resolved Brillouin light scattering microscopy. A rejection frequency band was clearly observed. The band gap frequency was controlled by the applied magnetic field. The measured spin-wave intensity as a function of frequency and propagation distance is in good agreement with a model calculation.