Bioactive glasses are a class of inorganic biomaterials widely used in bone tissue engineering and regenerative medicine. Once implanted in the human body, these biomaterials react with the body fluid resulting in the formation of a surface hydroxyapatite (HA) layer, which exhibits the ability to form a stable chemical bond with the adjacent living bone tissue. The experimental evaluation of the degradation of bioactive glasses in contact with body fluid requires long-term in vitro assays. In this work, a novel mathematical model is proposed to numerically analyze the dissolution and bioactivity of bioactive glasses in relevant conditions for their in vitro and in vivo applications. A detailed framework is described for the numerical implementation using the Voxel-FEM method, in order to account for the microstructural evolution as consequence of degradation and HA layer formation. Two examples of application are highlighted, showing the suitability and usefulness of the proposed model for the evaluation of bioactive glasses in tissue engineering applications.