The use of Remote patient monitoring (RPM) systems to monitor critically ill patients in the Intensive Care Unit (ICU) has enabled quality and real-time healthcare management. Fuzzy logic as an approach to designing RPM systems provides a means for encapsulating the subjective decision-making process of medical experts in an algorithm suitable for computer implementation. In this paper, a remote monitoring system for preterm in neonatal ICU incubators is modeled and simulated. The model was designed with 4 input variables (body temperature, heart rate, respiratory rate, and oxygen level saturation), and 1 output variable (action performed represented as ACT). ACT decides whether an alert is generated or not and also determines the message displayed when a notification is required. ACT classifies the clinical priority of the monitored preterm into 5 different fields: code blue, code red, code yellow, code green, and code black. The model was simulated using a fuzzy logic toolbox of MATLAB R2015A. About 216 IF_THEN rules were formulated to monitor the inputs data fed into the model. The performance of the model was evaluated using the confusion matrix to determine the model’s accuracy, precision, sensitivity, specificity, and false alarm rate. The experimental results obtained shows that the fuzzy-based system is capable of producing satisfactory results when used for monitoring and classifying the clinical statuses of neonates in ICU incubators.