This study was designed in a rat model to determine the hallmarks of possible permanent behavioral and structural brain alterations after a single moderate hypoxic insult. Eighty-two Wistar Han (RccHan: WIST) rats were randomly subjected to hypoxia (pO2 73 mmHg/2 h) or normoxia at the first postnatal day. The substantially increased blood lactate, a significantly decreased cytochrome-C-oxygenase expression in the brain, and depleted subventricular zone suggested a high vulnerability of subset of cell populations to oxidative stress and consequent tissue response even after a single, moderate, hypoxic event. The results of behavioral tests (open-field, hole-board, social-choice, and T-maze) applied at the 30–45th and 70–85th postnatal days revealed significant hyperactivity and a slower pace of learning in rats subjected to perinatal hypoxia. At 3.5 months after hypoxic insult, the histochemical examination demonstrated a significantly increased number of specific extracellular matrix—perineuronal nets and increased parvalbumin expression in a subpopulation of interneurons in the medial and retrosplenial cingulate cortex of these animals. Conclusively, moderate perinatal hypoxia in rats causes a long-lasting reorganization of the connectivity in the cingulate cortex and consequent alterations of related behavioral and cognitive abilities. This non-invasive hypoxia model in the rat successfully and complementarily models the moderate perinatal hypoxic injury in fetuses and prematurely born human babies and may enhance future research into new diagnostic and therapeutic strategies for perinatal medicine.