Neural Architecture Search (NAS) has proven effective in discovering new Convolutional Neural Network (CNN) architectures, particularly for scenarios with well-defined accuracy optimization goals. However, previous approaches often involve time-consuming training on super networks or intensive architecture sampling and evaluations. Although various zero-cost proxies correlated with CNN model accuracy have been proposed for efficient architecture search without training, their lack of hardware consideration makes it challenging to target highly resource-constrained edge devices such as microcontroller units (MCUs). To address these challenges, we introduce MONAS, a novel hardware-aware zero-shot NAS framework specifically designed for MCUs in edge computing. MONAS incorporates hardware optimality considerations into the search process through our proposed MCU hardware latency estimation model. By combining this with specialized performance indicators (proxies), MONAS identifies optimal neural architectures without incurring heavy training and evaluation costs, optimizing for both hardware latency and accuracy under resource constraints. MONAS achieves up to a 1104x improvement in search efficiency over previous work targeting MCUs and can discover CNN models with over 3.23x faster inference on MCUs while maintaining similar accuracy compared to more general NAS approaches.