Background: ICU admission due to COVID-19 may result in cognitive and physical impairment. We investigated the long-term cognitive and physical status of Danish ICU patients with COVID-19. Methods: We included all patients with COVID-19 admitted to Danish ICUs between March 10 and May 19, 2020. Patients were the contacted prospectively at 6 and 12 months for follow-up. Our primary outcomes were cognitive function and frailty at 6 and 12 months after ICU admission, estimated by the Mini Montreal Cognitive Assessment, and the Clinical Frailty Scale. Secondary outcomes were 6- and 12-month mortality, health-related quality of life (HRQoL) assessed by EQ-5D-5L, functional status (Barthel activities of daily living and Lawton–Brody instrumental activities of daily living), and fatigue (Fatigue Assessment Scale). The study had no information on pre-ICU admission status for the participants. Results: A total of 326 patients were included. The 6- and 12-month mortality was 37% and 38%, respectively. Among the 204 six-month survivors, 105 (51%) participated in the 6-month follow-up; among the 202 twelve-month survivors, 95 (47%) participated in the 12-month follow-up. At 6 months, cognitive scores indicated impairment for 26% (95% confidence interval [CI], 11.4–12.4) and at 12 months for 17% (95% CI, 12.0–12.8) of participants. Frailty was indicated in 20% (95% CI, 3.4–3.9) at 6 months, and for 18% (95% CI, 3.3–3.8) at 12 months. Fatigue was reported by 52% at 6 months, and by 47% at 12 months. For HRQoL, moderate, severe, or extreme health problems were reported by 28% at 6 months, and by 25% at 12 months. Conclusion: Long-term cognitive, functional impairment was found in up to one in four of patients surviving intensive care for COVID-19. Fatigue was present in nearly half the survivors at both 6 and 12 months. However, pre-ICU admission status of the patients was unknown.