The ability to detect when a system undergoes an incipient fault is of paramount importance in preventing a critical failure. Classic methods for fault detection (including model-based and data-driven approaches) rely on thresholding error statistics or simple input-residual dependencies but face difficulties with non-linear or non-Gaussian systems. Behavioral methods (e.g., those relying on digital twins) address these difficulties but still face challenges when faulty data is scarce, decision guarantees are required, or working with already-deployed models is required. In this work, we propose an information-driven fault detection method based on a novel concept drift detector, addressing these challenges. The method is tailored to identifying drifts in input-output relationships of additive noise models (i.e., model drifts) and is based on a distribution-free mutual information (MI) estimator. Our scheme does not require prior faulty examples and can be applied distribution-free over a large class of system models. Our core contributions are twofold. First, we demonstrate the connection between fault detection, model drift detection, and testing independence between two random variables. Second, we prove several theoretical properties of the proposed MI-based fault detection scheme: (i) strong consistency, (ii) exponentially fast detection of the non-faulty case, and (iii) control of both significance levels and power of the test. To conclude, we validate our theory with synthetic data and the benchmark dataset N-CMAPSS of aircraft turbofan engines. These empirical results support the usefulness of our methodology in many practical and realistic settings, and the theoretical results show performance guarantees that other methods cannot offer.