In this paper, we address the problem of frequency offset and channel gain estimation for frequency-selective multi-input multi-output (MIMO) correlated fading channels. A maximum-likelihood (ML) frequency offset (FO) estimator is proposed by using the Bayesian approach. We show that the proposed FO estimator is efficient and asymptotically optimal. Based on the FO estimate, we derive the linear minimum mean square error (LMMSE) channel estimator and analytically investigate the effect of frequency offset estimation error on the mean square error (MSE) performance of the channel estimator. Finally, the performances of the FO and channel estimation are evaluated by simulation results.