Epithelial injury induces rapid recruitment of antimicrobial leukocytes to the wound site. In zebrafish larvae, activation of the epithelial NADPH oxidase Duox at the wound margin is required early during this response. Before injury, leukocytes are near the vascular region, that is, $100-300 mm away from the injury site. How Duox establishes long-range signaling to leukocytes is unclear. We conceived that extracellular hydrogen peroxide (H 2 O 2 ) generated by Duox diffuses through the tissue to directly regulate chemotactic signaling in these cells. But before it can oxidize cellular proteins, H 2 O 2 must get past the antioxidant barriers that protect the cellular proteome. To test whether, or on which length scales this occurs during physiological wound signaling, we developed a computational method based on reaction-diffusion principles that infers H 2 O 2 degradation rates from intravital H 2 O 2 -biosensor imaging data. Our results indicate that at high tissue H 2 O 2 levels the peroxiredoxin-thioredoxin antioxidant chain becomes overwhelmed, and H 2 O 2 degradation stalls or ceases. Although the wound H 2 O 2 gradient reaches deep into the tissue, it likely overcomes antioxidant barriers only within $30 mm of the wound margin. Thus, Duox-mediated long-range signaling may require other spatial relay mechanisms besides extracellular H 2 O 2 diffusion.