As with anything connected to the internet, industrial Internet of Things (IIoT) devices are also subject to severe cybersecurity threats because an adversary could exploit vulnerabilities in their internal software to perform malicious attacks. Despite the promising results of deep learning-based approaches, most solutions can only detect the presence of a vulnerability but fail to pinpoint its corresponding type. Recently, TreeVul formalizes the task as a hierarchical multilabel classification problem to predict complete coarse-to-fine vulnerability type hierarchy. Yet, the TreeVul approach is still inaccurate and neglects samples labeled at coarse categories. In this article, we propose HierVul, a novel hierarchy-aware representation learning approach for IIoT vulnerability classification. Specifically, to make full use of vulnerable samples labeled at any granularity, HierVul constructs hierarchy-specific extractors as well as classifiers to disentangle level-wise vulnerability features from the code representation learning network backbone, and maximizes their marginal probability in the probability space constrained by the Common Weakness Enumeration tree hierarchy. Furthermore, considering that the distinction between two vulnerability types at the same level of abstraction becomes smaller and smaller as the refinement of classification granularity, HierVul leverages residual connections to add parent-level coarser-grained features to child-level finer-grained features to transfer hierarchical knowledge across levels. The experimental results show that HierVul achieves 15.25%, 45.16%, and 14.52% relative improvement over TreeVul on Weight F1, Macro F1, and PF, respectively, indicating the effectiveness of HierVul in the practical scenario.