Infants with fragile skin are patients who would benefit from non-contact vital sign monitoring due to the avoidance of potentially harmful adhesive electrodes and cables. Non-contact vital signs monitoring has been studied in clinical settings in recent decades. However, studies on infants in the Neonatal Intensive Care Unit (NICU) are still limited. Therefore, we conducted a single-center study to remotely monitor the heart rate (HR) and respiratory rate (RR) of seven infants in NICU using a digital camera. The region of interest (ROI) was automatically selected using a convolutional neural network and signal decomposition was used to minimize the noise artefacts. The experimental results have been validated with the reference data obtained from an ECG monitor. They showed a strong correlation using the Pearson correlation coefficients (PCC) of 0.9864 and 0.9453 for HR and RR, respectively, and a lower error rate with RMSE 2.23 beats/min and 2.69 breaths/min between measured data and reference data. A Bland–Altman analysis of the data also presented a close correlation between measured data and reference data for both HR and RR. Therefore, this technique may be applicable in clinical environments as an economical, non-contact, and easily deployable monitoring system, and it also represents a potential application in home health monitoring.