This paper addresses the fundamental performance limits of Integrated Sensing and Communication (ISAC) systems by introducing a novel converse bound based on rate-distortion theory. This rate-distortion bound (RDB) overcomes the restrictive regularity conditions of classical estimation theory, such as the Bayesian Cramér-Rao Bound (BCRB). The proposed framework is broadly applicable, holding for arbitrary parameter distributions and distortion measures, including mean-squared error and probability of error. The bound is proved to be tight in the high sensing noise regime and can be strictly tighter than the BCRB in the low sensing noise regime. The RDB's utility is demonstrated on two challenging scenarios: Nakagami fading channel estimation, where it provides a valid bound even when the BCRB is inapplicable, and a binary occupancy detection task, showcasing its versatility for discrete sensing problems. This work provides a powerful and general tool for characterizing the ultimate performance tradeoffs in ISAC systems.