In the context of detecting changes in structural systems, several vibration‐based damage detection methods have been proposed and successfully applied to both mechanical and civil structures over the past years. These methods involve computing data‐based features, which are then evaluated in statistical tests to detect damages. While being sensitive to damages, the data‐based features are affected by changes in the ambient excitation properties that potentially lead to false alarms in the statistical tests, a characteristic that renders their use impractical for structural monitoring. In this paper, a damage detection method is presented that is robust to changes in the covariance of the ambient excitation. The proposed approach is based on the Mahalanobis distance of output covariance Hankel matrices, which are normalized with respect to possibly changing excitation properties. The statistical properties of the developed damage feature are reported and used for efficient hypothesis testing. Its robustness towards changes in the excitation covariance is illustrated on numerical simulations and successfully tested on a numerical offshore foundation model.