A smart city is an intelligent space, in which large amounts of data are collected and analyzed using low-cost sensors and automatic algorithms. The application of artificial intelligence and Internet of Things (IoT) technologies in electronic health (E-health) can efficiently promote the development of sustainable and smart cities. The IoT sensors and intelligent algorithms enable the remote monitoring and analyzing of the healthcare data of patients, which reduces the medical and travel expenses in cities. Existing deep learning-based methods for healthcare sensor data classification have made great achievements. However, these methods take much time and storage space for model training and inference. They are difficult to be deployed in small devices to classify the physiological signal of patients in real time. To solve the above problems, this paper proposes a micro time series classification model called the micro neural network (MicroNN). The proposed model is micro enough to be deployed on tiny edge devices. MicroNN can be applied to long-term physiological signal monitoring based on edge computing devices. We conduct comprehensive experiments to evaluate the classification accuracy and computation complexity of MicroNN. Experiment results show that MicroNN performs better than the state-of-the-art methods. The accuracies on the two datasets (MIT-BIH-AR and INCART) are 98.4% and 98.1%, respectively. Finally, we present an application to show how MicroNN can improve the development of sustainable and smart cities.