In this work, we study out-of-distribution (OOD) generalization in meta-reinforcement learning from an information-theoretic perspective. We begin by establishing OOD generalization bounds for meta-supervised learning under two distinct distribution shift scenarios: standard distribution mismatch and a broad-to-narrow training setting. Building on this foundation, we formalize the generalization problem in meta-reinforcement learning and establish fine-grained generalization bounds that exploit the structure of Markov Decision Processes. Lastly, we analyze the generalization performance of a gradient-based meta-reinforcement learning algorithm.