Evidence in humans and rodents suggests that perinatal exposure to selective serotonin reuptake inhibitor (SSRI) antidepressants can have serious long‐term consequences in offspring exposed in utero or infancy via breast milk. In spite of this, there is limited knowledge of how perinatal SSRI exposure impacts brain development and adult behaviour. Children exposed to SSRIs in utero exhibit increased internalizing behaviour and abnormal social behaviour between the ages of 3 and 6, and increased risk of depression in adolescence; however, the neurobiological changes underlying this behaviour are poorly understood. In rodents, perinatal SSRI exposure perturbs hippocampal gene expression and alters adult emotional behaviour (including increased depression‐like behaviour). The present study demonstrates that perinatal exposure to the SSRI paroxetine leads to DNA hypomethylation and reduces DNA methyltransferase 3a (Dnmt3a) mRNA expression in the hippocampus during the second and third weeks of life. Next‐generation sequencing identified numerous differentially methylated genomic regions, including altered methylation and transcription of several dendritogenesis‐related genes. We then tested the hypothesis that transiently decreasing Dnmt3a expression in the early postnatal hippocampus would mimic the behavioural effects of perinatal SSRI exposure. We found that siRNA‐mediated knockdown of Dnmt3a in the dentate gyrus during the second to third week of life produced greater depression‐like behaviour in adult female (but not male) offspring, akin to the behavioural consequences of perinatal SSRI exposure. Overall, these data suggest that perinatal SSRI exposure may increase depression‐like behaviours, at least in part, through reduced Dnmt3a expression in the developing hippocampus.