Out-of-distribution (OOD) detection in deep learning has traditionally been framed as a binary task, where samples are either classified as belonging to the known classes or marked as OOD, with little attention given to the semantic relationships between OOD samples and the in-distribution (ID) classes. We propose a framework for detecting and classifying OOD samples in a given label hierarchy. Specifically, we aim to predict OOD data to their correct internal nodes of the label hierarchy, whereas the known ID classes should be predicted as their corresponding leaf nodes. Our approach leverages the label hierarchy to create a probabilistic model and we implement this model by using networks trained for ID classification at multiple hierarchy depths. We conduct experiments on three datasets with predefined label hierarchies and show the effectiveness of our method. Our code is provided as supplementary material.