A microphone array beamformer combined with a post-filter estimation based on spatial smoothing can deliver good noise attenuation preserving the speech component, however, with disturbing musical tones. On the other hand, the temporal smoothing of the decision-directed (DD) a priori signal-to-noise ratio (SNR) estimation for single-channel noise reduction can suppress musical tones well, however, with speech distortion particularly in speech onset. Based on these facts, we derive a new data-driven multichannel a priori SNR estimation based on both spatial and temporal smoothing for the use in a beamformer post-filter. The new a priori SNR estimation is able to find an optimum compromise between noise attenuation, quality of the speech component, and musical tones suppression.