Structural Health Monitoring (SHM) is essential to ensure the structural safety of masonry constructions, as it can enable the early detection of signs of material deterioration and structural damage. However, in common practice, the effectiveness of SHM systems is often limited by the scarcity of data referring to damage conditions. This lack of information reduces the possibility of developing accurate predictive models for novelty detection analysis, thus limiting the early identification of structural pathologies that affect masonry constructions. To address this challenge, finite element micromechanical modelling of an in-plane loaded archetypal masonry panel is proposed in this paper, simulating different types of damage with varying levels of severity to construct a damage classifier that can generalise to real masonry walls. Monitoring data are generated numerically by simulating the use of smart bricks, a new class of sensors for SHM of masonry constructions, to collect strain measurements at key points of the masonry panel under different damage scenarios. A damage classification system, capable of accurately identifying different types of damages (e.g., induced by seismic events or differential foundation settlements) and their severity, is developed using Domain Adversarial Neural Networks (DANN) trained with smart bricks’ strain measurements from numerical simulations. The obtained results demonstrate the effectiveness of the proposed approach in training the DANN for accurate predictions of structural damage to masonry constructions.