Abstract: Microwave kinetic inductance detectors have great potential for large, very sensitive detector arrays for use in, for example, submillimeter imaging. Being intrinsically readout in the frequency domain, they are particularly suited for frequency domain multiplexing allowing ~1000 s of devices to be readout with one pair of coaxial cables. However, this moves the complexity of the detector from the cryogenics to the warm electronics. We present here the concept and experimental demonstration of the use of fast Fourier transform spectrometer readout, showing no deterioration of the noise performance compared to the low noise analog mixing while allowing high multiplexing ratios.