The task of extracting drug entities and possible interactions between drug pairings is known as Drug–Drug Interaction (DDI) extraction. Computer-assisted DDI extraction with Machine Learning techniques can help streamline this expensive and time-consuming process during the drug development cycle. Over the years, a variety of both traditional and Neural Network-based techniques for the extraction of DDIs have been proposed. Despite the introduction of several successful strategies, obtaining high classification accuracy is still an area where further progress can be made. In this work, we present a novel Knowledge Graph (KG) based approach that utilizes a unique graph structure in combination with a Transformer-based Language Model and Graph Neural Networks to classify DDIs from biomedical literature. The KG is constructed to model the knowledge of the DDI Extraction 2013 benchmark dataset, without the inclusion of additional external information sources. Each drug pair is classified based on the context of the sentence it was found in, by utilizing transfer knowledge in the form of semantic representations from domain-adapted BioBERT weights that serve as the initial KG states. The proposed approach was evaluated on the DDI classification task of the same dataset and achieved a F1-score of 79.14% on the four positive classes, outperforming the current state-of-the-art approach.