In this paper, MODWT is used to decompose the Electrocardiography (ECG) signals and to identify the changes of R waves in the noisy input ECG signal. The MODWT is used to handle the arbitrary changes in the input signal. The R wave's detctected by the proposed framework is used by the doctors and careholders to take necessary action for the patients. MATLAB simulink model is used to develop the simulation model for the MODWT method. The performance of the MODWT based remote health monitoring system method is comparatively analyzed with other ECG monitoring approaches such as Haar Wavelet Transformation (HWT) and Discrete Wavelet Transform (DWT). Sensitivity, specificity, and Receiver Operating Characteristic (ROC) curve are calculated to evaluate the proposed Internet of Things with MODWT based ECG monitoring system. We have used MIT-BIH Arrythmia Database to perform the experiments.