Piezo-actuated MEMS loudspeakers are promising transducers for compact audio arrays with a high transducer density, yet their spatial radiation properties remain largely unexplored in the context of array processing. In this paper, we present a modeling and experimental characterization study of the free-field directivity of a commercial piezoelectric MEMS loudspeaker. Angular frequency-response measurements on five devices, acquired over the azimuth and elevation planes, show that the source departs from omnidirectional behavior already in the lower part of the operating frequency range and becomes increasingly directive with frequency. To describe this behavior, a compact planar model is introduced through a truncated Fourier-series expansion of the measured complex response. The identified element model is then embedded into a far-field formulation for planar loudspeaker arrays and validated on a measured five-element linear configuration. The results show good agreement between the predicted and measured array responses, supporting directivity-aware element modeling as a relevant ingredient for MEMS loudspeaker array simulation and beamformer design.