Magnetic microcalorimeters (MMCs) are cryogenic, energy-dispersive single-particle detectors providing excellent energy resolution, intrinsically fast signal rise time, quantum efficiency close to 100%, large dynamic range as well as almost ideal linear response. One of the remaining challenges to be overcome to ultimately allow for the utilization of large-scale MMC based detector arrays with thousands to millions of individual pixels is the realization of a SQUID based multiplexing technique particularly tailored for MMC readout. Within this context, we report on the first demonstration of a frequency-division multiplexed readout of an MMC based detector array using both, a custom microwave SQUID multiplexer as well as a dedicated software-defined radio (SDR) readout electronics. We successfully performed a simultaneous readout up to eight multiplexer channels, each monitoring two detector pixels. We show that the signal shape is not changed as compared to a dc-SQUID readout and that similar values for the energy resolution can be obtained. Nevertheless, we observed an influence of the internal quality factor of the microwave resonators used for frequency encoding on the energy resolution that affects the resolution of the co-added sum spectrum.