ICD coding is designed to assign the disease codes to electronic health records (EHRs) upon discharge, which is crucial for billing and clinical statistics. In an attempt to improve the effectiveness and efficiency of manual coding, many methods have been proposed to automatically predict ICD codes from clinical notes. However, most previous works ignore the decisive information contained in structured medical data in EHRs, which is hard to be captured from the noisy clinical notes. In this paper, we propose a Tree-enhanced Multimodal Attention Network (TreeMAN) to fuse tabular features and textual features into multimodal representations by enhancing the text representations with tree-based features via the attention mechanism. Tree-based features are constructed according to decision trees learned from structured multimodal medical data, which capture the decisive information about ICD coding. We can apply the same multi-label classifier from previous text models to the multimodal representations to predict ICD codes. Experiments on two MIMIC datasets show that our method outperforms prior state-of-the-art ICD coding approaches. The code is available at https://github.com/liu-zichen/TreeMAN.