The exponential growth of Internet of Things (IoT) devices has heightened the demand for scalable and low-latency security solutions. Traditional cloud-based intrusion detection systems (IDS) struggle to meet the real-time processing requirements of these dynamic environments. In this study, we present FIRE, a novel Fog-based Intrusion Detection framework for Real-time security in IoT Environments, which leverages fog computing and supervised learning to detect and classify network intrusions with low latency. The FIRE framework operates in three stages: i) data aggregation using session-based and time-based sliding window techniques; ii) supervised model inference leveraging dimensionality reduction and multiple classification algorithms including Random Forest, XGBoost, and deep neural networks; and iii) simulation of real-time detection using sequential, parallel, and continuous data processing in a fog-based setup. Experimental results demonstrate that FIRE achieves high detection accuracy (up to 99.8%) while maintaining real-time performance, with lightweight models such as Decision Trees and XGBoost processing chunks in under 0.05 s. Comparative analysis further shows that fog-based deployment significantly outperforms our cloud-based simulation, reducing latency by up to 7.7 \(\times \) in sequential processing environments. The proposed framework offers a scalable and efficient solution for real-time IoT security, and sets the foundation for future work in explainable AI integration and adaptive threat response in fog environments.