As Artificial Intelligence (AI) becomes increasingly integral to various sectors, organizations are striving to harness AI's potential for innovation and operational enhancement. However, a major challenge lies in establishing effective incident management frameworks to mitigate the inherent risks associated with AI systems. Our study addresses this gap by developing a framework for characterizing AI incidents, essential for informed incident management and regulatory compliance. We conduct an in-depth analysis of real-world AI incidents, synthesizing insights from existing literature on incident management and data breaches. The resulting framework highlights key dimensions such as incident causes, loci, impacts, and failure modes, providing a structured approach to understanding AI incident profiles. This research offers a valuable tool for researchers and organizations to analyze AI incidents and formulate response strategies. Our findings contribute to the broader discourse on AI risk management by integrating both technical and organizational perspectives, paving the way for responsible AI deployment.