The Internet of Things (IoT) will connect not only computers and mobile devices, but it will also interconnect smart buildings, homes, and cities, as well as electrical grids, gas, and water networks, automobiles, airplanes, etc. IoT will lead to the development of a wide range of advanced information services that need to be processed in real-time and require large storage and computational power. The integration of IoT with Cloud Computing can bring not only the computational requirements, but it also enable IoT services to be pervasive, cost-effective, and can be accessed from anywhere and at any time. However, IoT applications will introduce grand security challenges due to the increase in the attack surface. Current approaches do not handle cybersecurity from a holistic point of view; hence a systematic cybersecurity mechanism needs to be adopted when designing IoT applications. In this paper, we present a framework to deploy highly secure IoT applications for Smart Infrastructures. Our approach is based on the Anomaly Behavior Analysis (ABA) methodology and Autonomic Computing paradigm to detect any threat in our framework. Our preliminary experimental results show that our approach can be used to detect threats and protect IoT premises and services.