Hybrid Autoregressive Transducer (HAT) is a recently proposed end-to-end acoustic model that extends the standard Recurrent Neural Network Transducer (RNN-T) for the purpose of the external language model (LM) fusion. In HAT, the blank probability and the label probability are estimated using two separate probability distributions, which provides a more accurate solution for internal LM score estimation, and thus works better when combining with an external LM. Previous work mainly focuses on HAT model training with the negative log-likelihood loss, while in this paper, we study the minimum word error rate (MWER) training of HAT -- a criterion that is closer to the evaluation metric for speech recognition, and has been successfully applied to other types of end-to-end models such as sequence-to-sequence (S2S) and RNN-T models. From experiments with around 30,000 hours of training data, we show that MWER training can improve the accuracy of HAT models, while at the same time, improving the robustness of the model against the decoding hyper-parameters such as length normalization and decoding beam during inference.