BACKGROUND AND OBJECTIVES: The extent and burden of postacute psychiatric and neurologic manifestations of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection are not yet fully understood. To evaluate the association between SARS-CoV-2 infection and postacute manifestations of psychiatric and neurologic disorders, we conducted a nationwide cohort study including the entire Danish population aged 12 years or older on March 1, 2020. METHODS: Individuals were followed up for SARS-CoV-2 infection and diagnosis of subsequent psychiatric and neurologic disorders from March 1, 2020, to January 31, 2023, using the Danish nationwide coronavirus disease 2019 (COVID-19) test surveillance database and the Danish National Patient Registry. The main period of interest was 1-12 months after infection. Incidence rate ratios (IRRs) of new onset of 11 psychiatric and 30 neurologic disorders were calculated by comparing incidence rates of disorders between SARS-CoV-2-positive individuals and individuals without a positive test (nonpositive individuals). Stratified analyses were conducted according to COVID-19 vaccination status, variant period, age, sex, and severity of infection. RESULTS: Overall, 1,775,639 individuals in the study cohort (n = 3,239,008) were tested SARS-CoV-2 positive during follow-up. SARS-CoV-2-positive individuals compared with nonpositive individuals were at 24% reduced risk of any psychiatric disease (IRR 0.76, 95% CI 0.74-0.78) in the postacute period. The risk of any neurologic disorder was slightly higher among SARS-CoV-2-positive individuals than among those without a positive test (IRR 1.05, 95% CI 1.04-1.07). IRRs for specific disorders varied considerably from a 3.9-fold increased risk of change in sense of smell or taste (IRR 3.91, 95% CI 2.77-5.53) to a 29% reduced risk of dementia (IRR 0.71, 95% CI 0.65-0.78). The severity of infection and vaccination status, more so than age, sex, and variant, were found to significantly influence the stratified IRRs. Compared with nonpositive individuals, hospitalized patients with COVID-19 were at a 2.1-fold (IRR 2.05, 95% CI 1.78-2.37) increased risk of psychiatric disorders and at a 2.4-fold increased risk of neurologic disorders (IRR 2.44, 95% CI 2.29-2.60). DISCUSSION: Our study does not support previous findings of substantial postacute neurologic and psychiatric morbidities among the general population of SARS-CoV-2-infected individuals, but does corroborate an elevated risk among the most severe cases with COVID-19.