COPD is a progressive disease that may lead to death if not diagnosed and treated at an early stage. The examination of vital signs such as respiration rate is a promising approach for the detection of COPD. However, simultaneous consideration of the demographic and medical characteristics of patients is very important for better results. The objective of this research is to investigate the capability of UWB radar as a non-invasive approach to discriminate COPD patients from healthy subjects. The non-invasive approach is beneficial in pandemics such as the ongoing COVID-19 pandemic, where a safe distance between people needs to be maintained. The raw data are collected in a real environment (a hospital) non-invasively from a distance of 1.5 m. Respiration data are then extracted from the collected raw data using signal processing techniques. It was observed that the respiration rate of COPD patients alone is not enough for COPD patient detection. However, incorporating additional features such as age, gender, and smoking history with the respiration rate lead to robust performance. Different machine-learning classifiers, including Naïve Bayes, support vector machine, random forest, k nearest neighbor (KNN), Adaboost, and two deep-learning models—a convolutional neural network and a long short-term memory (LSTM) network—were utilized for COPD detection. Experimental results indicate that LSTM outperforms all employed models and obtained 93% accuracy. Performance comparison with existing studies corroborates the superior performance of the proposed approach.