Reactive oxygen species are toxic byproducts of aerobic respiration produced during cell growth. They also are an important component of plant defenses to inhibit microbial pathogens. Tolerance to oxidative stress contributes to viability and pathogenicity of plant pathogens. However, the complex molecular network of oxidative stress responses hinders identification of the genes contributing to variation in this trait. Variation in genes affecting responses to oxidative stress is likely to affect the evolutionary potential of pathogen tolerance to host defences. Here, we employed a forward genetic approach to investigate the genetic architecture of oxidative stress tolerance in the fungal wheat pathogen Zymoseptoria tritici. By performing quantitative trait locus (QTL) mapping in two crosses, we identified several genomic regions associated with tolerance to oxidative stress, including a QTL having a large effect on growth under oxidative stress. We found evidence for a significant trade-off between growth under non-stressful conditions and growth inhibition under oxidative stress. We identified a large QTL associated with this trade-off and with growth under non-stressful conditions, suggesting that differences in fungal growth could result in different sensitivities to oxidative stress. Our results suggest that genes related to fungal growth could also contribute to variation in oxidative stress tolerance among fungal strains.