Smart healthcare systems that make use of abundant health data can improve access to healthcare services, reduce medical costs and provide consistently high-quality patient care. Medical dialogue systems that generate medically appropriate and human-like conversations have been developed using various pre-trained language models and a large-scale medical knowledge base based on Unified Medical Language System (UMLS). However, most of the knowledge-grounded dialogue models only use local structure in the observed triples, which suffer from knowledge graph incompleteness and hence cannot incorporate any information from dialogue history while creating entity embeddings. As a result, the performance of such models decreases significantly. To address this problem, we propose a general method to embed the triples in each graph into large-scalable models and thereby generate clinically correct responses based on the conversation history using the recently recently released MedDialog(EN) dataset. Given a set of triples, we first mask the head entities from the triples overlapping with the patient’s utterance and then compute the cross-entropy loss against the triples’ respective tail entities while predicting the masked entity. This process results in a representation of the medical concepts from a graph capable of learning contextual information from dialogues, which ultimately aids in leading to the gold response. We also fine-tune the proposed Masked Entity Dialogue (MED) model on smaller corpora which contain dialogues focusing only on the Covid-19 disease named as the Covid Dataset. In addition, since UMLS and other existing medical graphs lack data-specific medical information, we re-curate and perform plausible augmentation of knowledge graphs using our newly created Medical Entity Prediction (MEP) model. Empirical results on the MedDialog(EN) and Covid Dataset demonstrate that our proposed model outperforms the state-of-the-art methods in terms of both automatic and human evaluation metrics.