During sudden disaster events, accurately predicting public panic sentiment on social media is crucial for proactive governance and crisis management. Current efforts on this problem face three main challenges: lack of finely annotated data hinders emotion prediction studies, unmodeled risk perception causes prediction inaccuracies, and insufficient interpretability of panic formation mechanisms. We address these issues by proposing a Psychology-driven generative Agent framework (PsychoAgent) for explainable panic prediction based on emotion arousal theory. Specifically, we first construct a fine-grained open panic emotion dataset (namely COPE) via human-large language models (LLMs) collaboration to mitigate semantic bias. Then, we develop a framework integrating cross-domain heterogeneous data grounded in psychological mechanisms to model risk perception and cognitive differences in emotion generation. To enhance interpretability, we design an LLM-based role-playing agent that simulates individual psychological chains through dedicatedly designed prompts. Experimental results on our annotated dataset show that PsychoAgent improves panic emotion prediction performance by 12.6% to 21.7% compared to baseline models. Furthermore, the explainability and generalization of our approach is validated. Crucially, this represents a paradigm shift from opaque "data-driven fitting" to transparent "role-based simulation with mechanistic interpretation" for panic emotion prediction during emergencies. Our implementation is publicly available at: https://anonymous.4open.science/r/PsychoAgent-19DD.