In this paper, the uplink performance of Multi-User Multiple Input Multiple Output (MU-MIMO) Zero Forcing (ZF) receiver is investigated over correlated Rayleigh fading channels with channel estimation error. A mathematical expression for the sub-streams' output Signal to Noise Ratio (SNR) with transmit and receive-correlation is derived in the presence of erroneous channel estimates. Besides, an approximate and accurate expression for the Bit Error Rate (BER) of ZF receiver for 16-Quadrature Amplitude Modulation (QAM) with transmit-correlation is deduced in terms of the hypergeometric function. Subsequently, the developed analytical BER is verified by Monte-Carlo trails accounting various system parameters. The simulation results indicate that ZF receiver's BER relies solely on the transmit-correlation for the same number of transmit and receive-antennas at higher average SNR values per transmitted symbol (E_s/N₀). Also, a logarithmic and exponential growth in the BER is observed with an increase in the Mean Square estimation Error (MSE) and correlation coefficient, respectively.