Major depressive disorder is a psychiatric disease having approximately a 20% lifetime prevalence in adults in the United States (U.S.), as reported by Hasin et al. in JAMA Psichiatry 2018 75, 336–346. Symptoms include low mood, anhedonia, decreased energy, alteration in appetite and weight, irritability, sleep disturbances, and cognitive deficits. Comorbidity is frequent, and patients show decreased social functioning and a high mortality rate. Environmental and genetic factors favor the development of depression, but the mechanisms by which stress negatively impacts on the brain are still not fully understood. Several recent works, mainly published during the last five years, aim at investigating the correlation between treatment with fluoxetine, a non-tricyclic antidepressant drug, and the amelioration of oxidative stress. In this work, the antioxidant activity of fluoxetine was investigated using a computational protocol based on the density functional theory approach. Particularly, the scavenging of five radicals (HO•, HOO•, CH3OO•, CH2=CHOO•, and CH3O•) was considered, focusing on hydrogen atom transfer (HAT) and radical adduct formation (RAF) mechanisms. Thermodynamic as well as kinetic aspects are discussed, and, for completeness, two metabolites of fluoxetine and serotonin, whose extracellular concentration is enhanced by fluoxetine, are included in our analysis. Indeed, fluoxetine may act as a radical scavenger, and exhibits selectivity for HO• and CH3O•, but is inefficient toward peroxyl radicals. In contrast, the radical scavenging efficiency of serotonin, which has been demonstrated in vitro, is significant, and this supports the idea of an indirect antioxidant efficiency of fluoxetine.