The identification of Chronic kidney (CK) disease in the medical field is still acts as a challenging scenario in the recent years. Precise recognition of CK disease possess a significant aspect in rendering effective treatment to the patients. Various forms of approaches have been developed for the exact classification of CK disease, but still there emerges certain forms of demerits including, improper selection of features, necessity of high storage space, requirement of effective learning model, less accurate, high complexities with respect to time and cost. The presence of these drawbacks adversely decreases the overall model performance. Hence to overcome these complexities, a graph neural network based deep Q learning (GNN-DQL) approach is proposed for the effective classification of five different stages like normal, mild, moderate, severe and end. Initially, the data are gathered from different people with the help of biomedical sensors through Internet of medical things (IoMT). The data are pre-processed through Handling Missing Values, Categorical Data Encoding, Data Transformation and Outlier Detection to eradicate the unwanted distortions. The Glomerular Filtration rate (GFR) is calculated with respect to age and serum creatinine level. Then, GNN-DQL technique is adopted for enhancing the classification accuracy. The parameters are optimized through Adaptive Mayfly Optimization (AMO) method. The classification performance is analysed with respect to accuracy, precision, recall, specificity, F1 score, confusion matrix and so on using PYTHON simulation tool. The classification accuracy of 99.93% is attained in the CK disease classification of five different stages regarding the collected data.