A deep learning method based on Convolutional Variational Auto-Encoder (CVAE) has been trained to reconstruct the ambient vibration time history response of undamaged structures. Various evaluation metrics of vibration data from a structure were then calculated between the input and the CVAE reconstructed signals. Such metrics are the data Mean Square Error (MSE) and Original to Reconstructed Signal Ratio (ORSR) and can assess the state of damage of a building by quantifying the similarity between its ambient vibration response and the analogous signals acquired from verified undamaged structures. In particular, the proposed methodology was experimentally verified in a specimen of a typical Central Italy historic masonry building subjected to shaking table tests. Low-intensity white-noise vibration tests were performed to simulate ambient vibration data. The state of damage was estimated by calculating a widely accepted Damage Index (DI) based on the first mode frequency decay of the building. The results showed that the approach provided by the combination of machine learning methods is very promising in their potentialities of assessing the structural damage in typical historic masonry buildings.