The collective behaviour of cells in epithelial tissues is dependent on their mechanical properties. However, the contribution of tissue mechanics to wound healing in vivo remains poorly understood. Here we investigate the relationship between tissue mechanics and wound healing in live Drosophila wing imaginal discs and show that by tuning epithelial cell junctional tension, we can systematically alter the rate of wound healing. Coincident with the contraction of an actomyosin purse string, we observe cells flowing past each other at the wound edge by intercalating, reminiscent of molecules in a fluid, resulting in seamless wound closure. Using a cell-based physical model, we predict that a reduction in junctional tension fluidises the tissue through an increase in intercalation rate and corresponding reduction in bulk viscosity, in the manner of an unjamming transition. The resultant fluidisation of the tissue accelerates wound healing. Accordingly, when we experimentally reduce tissue tension in wing discs, intercalation rate increases and wounds repair in less time.