This study aimed to investigate psychological distress among patients hospitalized with a COVID-19 diagnosis in Denmark during the first 12 months of the pandemic and to assess changes in psychological distress in the three months following discharge. A single-center prospective observational survey study among patients hospitalized with a COVID-19 diagnosis between May 2020 and May 2021 was conducted. Participants completed a survey at three time points: at admission, and 1 and 3 months after discharge. Psychological distress was assessed by validated scales measuring symptoms related to depression, anxiety, stress, insomnia, post-traumatic stress disorder (PTSD), and health-related quality of life (HRQoL). In total, 95 patients were included. At admission, the proportion of patients with symptoms of depression was 43%, symptoms of anxiety 32%, moderate/high level of stress 39%, insomnia 52%, and probable/positive PTSD 19%. The burden of symptoms related to depression and anxiety decreased significantly over time, while there was no significant change over time in stress, insomnia, or PTSD. Suboptimal levels of physical and mental HRQoL were detected at admission but improved over time. Patients hospitalized due to COVID-19 during the first year of the pandemic experienced considerable levels of psychological distress at admission, with some improvements within 3 months after discharge.