Confinement during the COVID-19 pandemic has significantly impacted lifestyles worldwide. The aim of this study was to evaluate the effect of confinement on anxiety symptoms and sleep quality in people living in extreme southern latitudes. The Beck Anxiety Inventory (BAI) and the Pittsburgh Sleep Quality Index (PSQI) were administered to 617 people, 74.2% of whom were women. The sample was grouped according to confinement: the zone of confinement (CZ) (46.5%) and the zone of partial confinement (PZ) (53.5%). In addition, the sample was further categorized into four age subgroups (18–25 years; 26–40 years; 41–50 years; over 50 years). Higher levels of anxiety and worse sleep quality were found in the CZ group than in the PZ group. Women had higher levels of anxiety and worse sleep quality than men. A significant bidirectional relationship between anxiety and sleep quality was observed, even after controlling for sex. This study demonstrated that women and young adults were more vulnerable to the effects of confinement on anxiety symptoms and sleep quality in populations at southern latitudes.