Respiratory rate (RR) is a vital indicator for assessing the bodily functions and health status of patients. RR is a prominent parameter in the field of biomedical signal processing and is strongly associated with other vital signs such as blood pressure, heart rate, and heart rate variability. Various physiological signals, such as photoplethysmogram (PPG) signals, are used to extract respiratory information. RR is also estimated by detecting peak patterns and cycles in the signals through signal processing and deep-learning approaches. In this study, we propose an end-to-end RR estimation approach based on a third-generation artificial neural network model—spiking neural network. The proposed model employs PPG segments as inputs, and directly converts them into sequential spike events. This design aims to reduce information loss during the conversion of the input data into spike events. In addition, we use feedback-based integrate-and-fire neurons as the activation functions, which effectively transmit temporal information. The network is evaluated using the BIDMC respiratory dataset with three different window sizes (16, 32, and 64 s). The proposed model achieves mean absolute errors of 1.37 ± 0.04, 1.23 ± 0.03, and 1.15 ± 0.07 for the 16, 32, and 64 s window sizes, respectively. Furthermore, it demonstrates superior energy efficiency compared with other deep learning models. This study demonstrates the potential of the spiking neural networks for RR monitoring, offering a novel approach for RR estimation from the PPG signal.