This paper introduces NeuroGuard-V2X, a privacy-preserving network monitoring architecture for connected vehicles based on neuromorphic edge processing. By deploying event-driven spiking neural networks directly on vehicles, the proposed system analyzes temporal patterns in heterogeneous V2X communications without transmitting or storing sensitive network data. NeuroGuard-V2X enables real-time intrusion detection across DSRC, cellular, and Wi-Fi interfaces while maintaining low latency and energy consumption. Experimental results demonstrate high detection accuracy, significant reductions in data transmission, and ultra-low power usage, highlighting its suitability for secure and scalable vehicular systems.