In this paper, we make use of a phase-sensitive time domain reflectometry (phi-OTDR) sensor with 60-cm spatial resolution to detect the Lamb waves generated by a piezo-ceramic actuator in an aluminum plate. Furthermore, a machine learning algorithm based on Support Vector Machine (SVM) classifiers was employed for damage localization. We show that SVMs are able to identify the characteristics in Lamb wave signals that may be linked to damage location. This study makes full use of the rich information provided by the phi-OTDR sensor, extracting damaged data from diverse damage spots. The results indicate that the proposed technique has the potential to identify and locate damages in thin-plate structures.