The rapidly increasing volume of medical text data, including biomedical literature and clinical records, presents difficulties to biomedical researchers and clinical practitioners. Automatic text classification is an important means for managing medical text data. The main challenge in medical text classification is the complex terminology used in these documents. Therefore, it is critical to handle synonymy, polysemy, and multi-word concepts so that classification is based on the meaning of these documents. The solution to this problem of complex terminology helps in building systems with better access to relevant data, resulting in more effective utilisation of the existing information. In this paper, we present a simple and effective approach to address this challenge. A concept graph is automatically constructed and enriched for each medical text document with the help of a domain-specific similarity matrix that is built using Unified Medical Language System (UMLS) concepts in the training documents. Medical text documents are compared based on their enriched concept graphs using a graph kernel. Classification is then done based on the comparison result. The benefit of this approach is that it allows the incorporation of domain knowledge into the classification frame-work. The experiments on biomedical abstracts and clinical reports classification show the effectiveness of the proposed approach. Based on evaluation metrics of precision, recall and F1-scores, our method achieves a significantly higher classification performance than other widely used similarity measures for similarity-based text classification.