In this paper, we propose a minimum mean square error spectral estimator for clean speech spectral amplitudes that uses a Kalman filter to model the temporal dynamics of the spectral amplitudes in the modulation domain. Using a two-parameter Gamma distribution to model the prior distribution of the speech spectral amplitudes, we derive closed form expressions for the posterior mean and variance of the spectral amplitudes as well as for the associated update step of the Kalman filter. The performance of the proposed algorithm is evaluated on the TIMIT core test set using the perceptual evaluation of speech quality (PESQ) measure and segmental SNR measure and is shown to give a consistent improvement over a wide range of SNRs when compared to competitive algorithms.