Adaptation to rapid environmental changes must occur within a short-time scale. In this context, studies of invasive species may provide insights into the underlying mechanisms of rapid adaptation as these species have repeatedly encountered and adapted to novel environmental conditions. We investigated how invasive and noninvasive genotypes of Drosophila suzukii deal with oxidative stress at the phenotypic and molecular levels. We also studied the impact of transposable element (TE) insertions on the gene expression in response to stress. Our results show that flies from invasive areas (France and the United States) live longer in natural conditions than the ones from native Japanese areas. As expected, lifespan for all genotypes was significantly reduced following exposure to paraquat, but this reduction varied among genotypes (genotype-by-environment interaction) with invasive genotypes appearing more affected by exposure than noninvasive ones. A transcriptomic analysis of genotypes upon paraquat treatment detected many genes differentially expressed (DE). Although a small core set of genes were DE in all genotypes following paraquat exposure, much of the response of each genotype was unique. Moreover, we showed that TEs were not activated after oxidative stress and DE genes were significantly depleted of TEs. In conclusion, it is likely that transcriptomic changes are involved in the rapid adaptation to local environments. We provide new evidence that in the decade since the invasion from Asia, the sampled genotypes in Europe and the United States of D. suzukii diverged from the ones from the native area regarding their phenotypic and genomic response to oxidative stress.