Automatic biomedical annotation is essential for advancing medical research, diagnosis, and treatment. However, it presents significant challenges, especially when entities are not explicitly mentioned in the text, leading to difficulties in extraction of relevant information. These challenges are intensified by unclear terminology, implicit background knowledge, and the lack of labeled training data. Annotating with a specific ontology adds another layer of complexity, as it requires aligning text with a predefined set of concepts and relationships. Manual annotation is time-consuming and expensive, highlighting the need for automated systems to handle large volumes of biomedical data efficiently. In this paper, we propose an entailment-based zero-shot text classification approach to annotate biomedical text passages using the Homeostasis Imbalance Process (HOIP) ontology. Our method reformulates the annotation task as a multi-class, multi-label classification problem and uses natural language inference to classify text into related HOIP processes. Experimental results show promising performance, especially when processes are not explicitly mentioned, highlighting the effectiveness of our approach for ontological annotation of biomedical literature.