Background Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections lead to acute- and chronic Long COVID (LC) symptoms. However, few studies have addressed LC sequelae on brain functions. This study was aimed to examine if acute symptoms of coronavirus disease 2019 (COVID-19) would persist during LC, and if memory problems would be correlated with sleep, depressive mood, or anxious complaints. Methods Our work followed a cohort of 236 patients from two public hospitals of the Federal District in mid-western Brazil. Patients’ interviews checked for clinical symptoms during acute and LC (5–8 months after real-time reverse transcription polymerase chain reaction, RT-qPCR). Results Most cases were non-hospitalized individuals (86.3%) with a median age of 41.2 years. While myalgia (50%), hyposmia (48.3%), and dysgeusia (45.8%) were prevalent symptoms in acute phase, fatigue (21.6%) followed by headache (19.1%) and myalgia (16.1%) commonly occurred during LC. In LC, 39.8% of individuals reported memory complaints, 36.9% felt anxious, 44.9% felt depressed, and 45.8% had sleep problems. Furthermore, memory complaints were associated with sleep problems (adjusted OR 3.206; 95% CI 1.723–6.030) and depressive feelings (adjusted OR 3.981; 95% CI 2.068–7.815). Conclusions The SARS-CoV-2 infection leads to persistent symptoms during LC, in which memory problems may be associated with sleep and depressive complaints.