Embryos repair wounds rapidly, with no inflammation or scarring, in a process that involves polarization of the actomyosin cytoskeleton. Actomyosin polarization results in the assembly of a contractile cable around the wound that drives wound closure. Here, we demonstrate that a contractile actomyosin cable is not sufficient for rapid wound repair in Drosophila embryos. We show that wounding causes activation of the serine/threonine kinase p38 mitogen-activated protein kinase (MAPK) in the cells adjacent to the wound. p38 activation reduces the levels of wound-induced reactive oxygen species in the cells around the wound, limiting wound size. In addition, p38 promotes an increase in volume in the cells around the wound, thus facilitating the collective cell movements that drive rapid wound healing. Our data indicate that p38 regulates cell volumes through the sodium-potassium-chloride cotransporter NKCC1. Our work reveals cell growth and cell survival as cell behaviors critical for embryonic wound repair.