A respiratory disorder that attacks COVID-19 patients requires intensive supervision of medical practitioners during the isolation period. A non-contact monitoring device will be a suitable solution for reducing the spread risk of the virus while monitoring the COVID-19 patient. This study uses Frequency-Modulated Continuous Wave (FMCW) radar and Machine Learning (ML) to obtain respiratory information and analyze respiratory signals, respectively. Multiple subjects in a room can be detected simultaneously by calculating the Angle of Arrival (AoA) of the received signal and utilizing the Multiple Input Multiple Output (MIMO) of FMCW radar. Fast Fourier Transform (FFT) and some signal processing are implemented to obtain a breathing waveform. ML helps the system to analyze the respiratory signals automatically. This paper also compares the performance of several ML algorithms such as Multinomial Logistic Regression (MLR), Decision Tree (DT), Random Forest (RF), Support Vector Machine (SVM), eXtreme Gradient Boosting (XGB), Light Gradient Boosting Machine (LGBM), CatBoosting (CB) Classifier, Multilayer Perceptron (MLP), and three proposed stacked ensemble models, namely Stacked Ensemble Classifier (SEC), Boosting Tree-based Stacked Classifier (BTSC), and Neural Stacked Ensemble Model (NSEM) to obtain the best ML model. The results show that the NSEM algorithm achieves the best performance with 97.1% accuracy. In the real-time implementation, the system could simultaneously detect several objects with different breathing characteristics and classify the respiratory signals into five different classes.