In reality, this is no such thing as perfect channel estimation. But unfortunately, channel estimation errors have never been taken into account by existing soft-output minimum mean square error (MMSE) multiple-input multiple-output (MIMO) detector when calculating the log-likelihood ratio (LLR) for coded bits, i.e., the soft information. As a result, its performance can be substantially degraded. In this paper, we propose a novel soft-output MMSE MIMO detector under maximum likelihood (ML) channel estimation for receiver correlated MIMO wireless communication systems. Based on random vector theorem, this proposed detector takes channel estimation errors and receiver correlation into account when constructing MMSE filter and computing LLR of each coded bit. Furthermore, a simplified version of this proposed detector is provided so that the requirement of the MIMO correlation matrix is dropped. Simulation results show that the proposed novel detector outperforms existing soft-output MMSE MIMO detector with considerable margin, and the simplified version can nearly achieve the same performance as that of the original one.