Increased rates of anxiety and depression have been reported for older adults during the COVID-19 pandemic. However, little is known regarding the onset of mental health morbidity during the acute phase of the disease and the role of age as potential independent risk factor for psychiatric symptoms. The cross-sectional association between older age and psychiatric symptoms has been estimated in a sample of 130 patients hospitalized for COVID-19 during the first and second wave of the pandemic. Compared to younger patients, those who were 70 years of age or older resulted at a higher risk of psychiatric symptoms measured on the Brief Psychiatric Symptoms Rating Scale (BPRS) (adjusted (adj.) odds ratio (OR) 2.36, 95% confidence interval (CI) 1.05–5.30) and delirium (adj. OR 5.24, 95% CI 1.63–16.8)). No association was found between older age and depressive symptoms or anxiety. Age was associated with psychiatric symptoms independently of gender, marital status, history of psychiatric illness, severity of disease and cardiovascular morbidity. Older adults appear at high risk of developing psychiatric symptoms related to COVID-19 disease during hospital stay. Multidisciplinary preventive and therapeutic interventions should be implemented to reduce the risk of psychiatric morbidity and related adverse health care outcomes among older hospital inpatients with COVID-19.