Structural health monitoring for offshore wind turbines is imperative. Offshore wind energy is progressively attained at greater water depths, beyond 30 m, where jacket foundations are presently the best solution to cope with the harsh environment (extreme sites with poor soil conditions). Structural integrity is of key importance in these underwater structures. In this work, a methodology for the diagnosis of structural damage in jacket-type foundations is stated. The method is based on the criterion that any damage or structural change produces variations in the vibrational response of the structure. Most studies in this area are, primarily, focused on the case of measurable input excitation and vibration response signals. Nevertheless, in this paper it is assumed that the only available excitation, the wind, is not measurable. Therefore, using vibration-response-only accelerometer information, a data-driven approach is developed following the next steps: (i) the wind is simulated as a Gaussian white noise and the accelerometer data are collected; (ii) the data are pre-processed using group-reshape and column-scaling; (iii) principal component analysis is used for both linear dimensionality reduction and feature extraction; finally, (iv) two different machine-learning algorithms, k nearest neighbor (k-NN) and quadratic-kernel support vector machine (SVM), are tested as classifiers. The overall accuracy is estimated by 5-fold cross-validation. The proposed approach is experimentally validated in a laboratory small-scale structure. The results manifest the reliability of the stated fault diagnosis method being the best performance given by the SVM classifier.