Sargahydroquinoic acid (SHQA), a bioactive compound found in certain Sargassum species, exhibits significant health benefits. This study optimized the extraction of SHQA from Sargassum yezoense using response surface methodology (RSM) and evaluated its antioxidant effects through in vitro and in vivo assays. A Box–Behnken design (BBD) was effectively employed to investigate the effects of incubation temperature, time, and ethanol concentration on SHQA yield, achieving a high coefficient of determination (R² = 0.961). Analysis of variance (ANOVA) validated the model’s reliability (F = 13.86, p = 0.005) and highlighted ethanol concentration as a highly significant factor (p < 0.001). Optimal extraction conditions were identified as 52.8 °C, 8.3 h, and 74.1% ethanol. The SHQA-maximized extract (SME) contained 67.8 ± 0.6 mg SHQA/g and 25.00 ± 1.01 mg phloroglucinol equivalent/g. SME exhibited antioxidant capacity of 26.45 ± 0.66 mg and 28.74 ± 2.30 mg vitamin C equivalent/g in ABTS and DPPH assays, respectively, and 0.29 ± 0.02 mM FeSO₄ equivalent/g in the FRAP assay. Additionally, SME at 50 µg/mL and SHQA at 1 µg/mL inhibited reactive oxygen species (ROS) generation in an H₂O₂-induced zebrafish model. This study presents the first optimization of SHQA extraction using RSM and demonstrates SHQA’s ROS inhibition in a zebrafish model.