Full-thickness wounds are associated with high morbidity and mortality. Here, biodegradable bioactive glass (BG) fiber mats with glass composition 70SiO2-(30-x)CaO-xZnO (mol%), where x = 1, 3 or 5 mol%, were synthesized for wound healing applications, facilitating therapeutic zinc ion release along with silica species and calcium ions. Cell attachement (fibroblasts and endothelial cells) and controlled ion release from the fibres is expected to promote angiogenesis. BG fibers (0.19–0.32 μm diameter) were synthesized through sol-gel electrospinning into a 3D extracellular matrix (ECM)-mimicking mat, which favors the attachment and migration of cells compared to BG microparticles. Human dermal fibroblast (HDF) cell culture demonstrated no cytotoxicity when exposed to Zn-containing BG fibers (Zn-BG). Dissolution products of Zn-BG fibers containing 5 mol% ZnO promoted angiogenic factors (VEGF and bFGF) expression compared to Zn-free BG fibers. Zn-BG-HDF media (supernatant from the co-culture of Zn-BG dissolution products and HDFs 1:1 mixed with fresh endothelial cell medium) promoted the metabolic activity of human umbilical vein endothelial cells (HUVECs) compared to 70S30C-HDF media. All BG-HDF media increased cell migration compared to untreated DMEM-HDF media, with the highest migration observed in response to BG with 5 mol% ZnO. When immersed in DMEM for 24 h, Zn-BG released 0.5–6 μg mL−1 of Zn, which is a concentration range with potential to elicit other beneficial effects in wound healing, such as antibacterial activity, positive inflammatory response, and follicle regeneration. Results suggest that Zn-BG fiber mats could help the regeneration of full-thickness wounds.