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Considering the mechanisms capable of causing brain alterations in COVID-19, we aimed to study the occurrence of cognitive abnormalities in the months following hospital discharge. We recruited 38 (aged 22–74 years; 27 males) patients hospitalized for complications of SARS-CoV-2 infection in nonintensive COVID units. Participants underwent neuropsychological testing about 5 months after hospital discharge. Of all patients, 42.1% had processing speed deficits, while 26.3% showed delayed verbal recall deficits. Twenty-one percent presented with deficits in both processing speed and verbal memory. Bivariate analysis revealed a positive correlation between the lowest arterial oxygen partial pressure (PaO₂) to fractional inspired oxygen (FiO₂) (P/F) ratio during hospitalization and verbal memory consolidation performance (SRT-LTS score, r = 0.404, p = 0.027), as well as a positive correlation between SpO₂ levels upon hospital arrival and delayed verbal recall performance (SRT-D score, r_s = 0.373, p = 0.042). Acute respiratory distress syndrome (ARDS) during hospitalization was associated with worse verbal memory performance (ARDS vs. no ARDS: SRT-LTS mean score = 30.63 ± 13.33 vs. 44.50 ± 13.16, p = 0.007; SRT-D mean score = 5.95 ± 2.56 vs. 8.10 ± 2.62, p = 0.029). Cognitive abnormalities can frequently be found in COVID-19 patients 5 months after hospital discharge. Increased fatigability, deficits of concentration and memory, and overall decreased cognitive speed months after hospital discharge can interfere with work and daily activities.