Transformers are vital elements in electric systems. Although they are robust machines, they can suffer from different faults during their service life. In particular, special attention has been given to winding faults since they are the most important and vulnerable components. In this regard, the development and application of condition monitoring schemes for winding faults are required. It is well-known that vibration signals can provide information related to faults or changes in the mechanical properties of transformers; however, the extraction of fault information from these signals and the automatic diagnosis are not straightforward processes. Therefore, in this work, a new methodology to detect short-circuited turns (SCTs) in transformers using vibration signals is presented. As first step, a set of fractal dimension algorithms (FDAs), i.e. Katz, Higuchi, Box, and Sevcik, are investigated as potential fault indicators. In order to test if they are sensitive to the fault severity, a modified transformer to represent different levels of SCTs is used. Then, a data mining approach is applied to perform an automatic diagnosis, where the results provided by the decision tree-, naïve Bayes-, and k-nearest neighbor-based classifiers are compared. Results demonstrate that these indices can detect SCTs and be sensitive to the fault severity.