In this paper, a linear MMSE filter is derived for single-channel speech enhancement which is based on Nonnegative Matrix Factorization (NMF). Assuming an additive model for the noisy observation, an estimator is obtained by minimizing the mean square error between the clean speech and the estimated speech components in the frequency domain. In addition, the noise power spectral density (PSD) is estimated using NMF and the obtained noise PSD is used in a Wiener filtering framework to enhance the noisy speech. The results of the both algorithms are compared to the result of the same Wiener filtering framework in which the noise PSD is estimated using a recently developed MMSE-based method. NMF based approaches outperform the Wiener filter with the MMSE-based noise PSD tracker for different measures. Compared to the NMF-based Wiener filtering approach, Source to Distortion Ratio (SDR) is improved for the evaluated noise types for different input SNRs using the proposed linear MMSE filter.