Heart rate (HR) and respiration rate (RR) play an important role in the study of complex behaviors and their physiological correlations in non-human primates (NHPs). However, collecting HR and RR information is often challenging, involving either invasive implants or tedious behavioral training, and there are currently few established simple and non-invasive techniques for HR and RR measurement in NHPs owing to their stress response or indocility. In this study, we employed a frequency-modulated continuous wave (FMCW) radar to design a novel contactless HR and RR monitoring system. The designed system can estimate HR and RR in real time by placing the FMCW radar on the cage and facing the chest of both awake and anesthetized macaques, the NHP investigated in this study. Experimental results show that the proposed method outperforms existing methods, with averaged absolute errors between the reference monitor and radar estimates of 0.77 beats per minute (bpm) and 1.29 respirations per minute (rpm) for HR and RR, respectively. In summary, we believe that the proposed non-invasive and contactless estimation method could be generalized as a HR and RR monitoring tool for NHPs. Furthermore, after modifying the radar signal-processing algorithms, it also shows promise for applications in other experimental animals for animal welfare, behavioral, neurological, and ethological research.