Background: Studies examining preoperative anxiety in patients awaiting hand surgery are scarce. Preoperative anxiety is a common reaction and can have a negative impact on treatment outcomes. The aim of this study was to assess the level of anxiety in patients undergoing hand surgery as a one-day procedure and to investigate the associations between patients’ preoperative anxiety and selected sociodemographic, psychological, and clinical variables. Methods: We examined 121 patients (77.7% women) who were operated on in an ambulatory setting. The mean age was 52.6 years (range: 24–84 years). Preoperative anxiety was assessed according to the Amsterdam Preoperative Anxiety and Information Scale (APAIS). The Visual Analogue Scale was used to assess irritability, depression, and pain. Results: Univariate analyses showed significant correlations between patients’ preoperative anxiety and increased age, surgery within a year since diagnosis, the presence of rehabilitation in their medical history, higher irritability, and living in rural areas. Multivariate analyses showed significant associations between patients’ anxiety level and diagnosis of up to a year, a history of rehabilitation and the level of irritability. Conclusions: Patients undergoing hand surgery in an ambulatory surgery setting experience some preoperative anxiety. Younger patients, those with a shorter duration of disease, with a history of rehabilitation, those presenting intense irritability, and those living in rural areas may demand special attention.