Hypoxia has been reported to impair psychological functions, such as working memory and decision-making. However, few studies have examined hypoxia's effect on social cognition. Using a self-referential task, the present study investigated normobaric hypoxia's effect on the self-referential process. Additionally, we measured brain activity during the task with fNIRS and performed conventional univariate analysis with the general linear model (GLM) as well as homologous cortical functional connectivity analysis. The results revealed that normobaric hypoxia impaired recognition of adjectives in the other-reference condition but not in the self-reference. The GLM analysis did not detect differences in brain activity between the self- and other-reference conditions, suggesting that GLM analysis may not be suitable for examining self- and other-reference conditions' neural correlates. The homologous cortical connectivity analysis revealed that the connectivity's magnitude was greater in the self-reference than in the other-reference conditions in the normoxic group. However, such a decrease in connectivity in the other-reference conditions was not observed in the hypoxic group, possibly to compensate for cognitive decline induced by the hypoxia. Considering that homologous connectivity reflects the default mode network, which is supposedly linked to continuous self-reference, stable strength of the connectivity in the self-reference condition under the hypoxia may suggest robust nature of the self-reference process under normobaric hypoxia.