Cognitive dysfunction in schizophrenia (SZ) is thought to arise from neurodevelopmental abnormalities that include interneuron hypomyelination in the prefrontal cortex (PFC). Here we report that RNA-sequencing of the medial (m)PFC of the APO-SUS rat model with SZ-relevant cognitive inflexibility revealed antioxidant metabolism as the most-enriched differentially expressed pathway. Antioxidant-related gene expression was altered throughout postnatal development and preceded hypomyelination. Furthermore, reduced glutathione levels and increased mitochondria numbers were observed in the mPFC. Strikingly, chronic treatment with the glutathione precursor N-acetylcysteine (NAC) from postnatal days 5–90 restored not only antioxidant-related mRNA expression and mitochondria numbers, but also myelin-related mRNA expression and mPFC-dependent cognitive dysfunction, while blood glutathione levels remained unaffected. The promyelinating effect of NAC was at least partly due to a positive effect on oligodendrocyte lineage progression. Together, our findings highlight that oxidative stress may contribute to cognitive symptoms in the APO-SUS rat model of SZ and encourage antioxidant therapy in early phases of SZ.