The massive MIMO communication technology has been widely deployed in existing 5G communication, providing increased capacity, improved spectral efficiency, better signal quality, etc. Channel estimation is a complex task and most channel estimation techniques consider a channel as a white channel but practically channels are correlated. The MMSE estimation for massive MIMO channels has been developed for white channels and its performance degrades if the channels are correlated. In this paper, two techniques are proposed to overcome this problem. In the first technique, the regularization term is introduced in the standard MMSE technique to mitigate the problem. Whereas, in the second technique pre-whitening-based MMSE solution is proposed. More specifically, the knowledge of the channel correlation matrix is employed to pre-whiten the received data before applying the MMSE weight matrix. Simulation results show that both proposed algorithm performance is better than the existing MMSE technique but the pre-whitening MMSE solution is superior as compared to other algorithms.