Structural Health Monitoring (SHM) of wind turbines is still far from a practical and effective implementation. One of the main limitations is the access to long-term experimental data from operative systems, as well as the access to a computational counterpart (e.g., Finite Element (FE) model) for testing purposes. This work proposes an unsupervised learning approach based on Deep Neural Networks (DNNs) for structural damage detection in a wind turbine operating within an onshore wind farm. The target system belongs to a wind farm in Portugal, where a long-term acceleration dataset was recorded and postprocessed to estimate the modal properties (eigenfrequencies and eigenmodes). Since the available monitoring data corresponds to what we assume is the healthy state, an unsupervised approach is required to learn from the data. We propose a Variational Autoencoder (VAE) approach to compress the measured features (particularly the eigenfrequencies) into a latent space variable and subsequently expand them into the original data space with minimal loss of information. This approach can be seen as a single-class classifier, where we learn to represent and reconstruct data from a known class, and any measurement that comes from a different generation process (e.g., damaged system) will be raised as an outlier. Given the stochastic character of the architecture, we explore the damage detection capability during testing by comparing statistic indicators. In order to generate damage scenarios, we employ a simple FE model, from which some damage simulations are resolved. We prevent the modeling error from being transferred to the experimental data by obtaining the relative change between the healthy and the damaged synthetic scenarios. These ratios are free from modeling error and can be applied, assuming the similarity of the domains to the experimental data. The results demonstrate that the VAE successfully detects the presence of damage. For slight damage cases, we find some scenarios where the histogram from the reconstruction error in (i) the healthy and (ii) the damaged scenario are almost overlapped, indicating some limitations. We explore the Receiver Operating Curves (ROC), which represent one of the most extensively employed techniques to measure the capability of single-class classifiers.