Depression and anxiety after stroke negatively affect patient outcomes; however, health care professionals may overlook poststroke depression and anxiety while they focus on the physical disabilities of patients soon after a stroke. The purpose of this study was to investigate the prevalence and predictors of depression, anxiety, or both concurrently at one month after stroke. We conducted a cross-sectional, descriptive study in a sample of 231 hospitalized patients with ischemic stroke in Korea. Data were collected by interviews using a series of structured questionnaires in addition to clinical data retrieved from patients’ medical records. More than 70% were identified as depressed, 45.9% experienced anxiety, and 43.7% had concurrent depression and anxiety. Using a multiple logistic regression analysis, we identified anxiety as a predictor of depression; depression as a predictor of anxiety; and female sex, headaches, and swallowing difficulty as predictors of the comorbidity of depression and anxiety. Periodical screenings for poststroke depression and anxiety from an early stage in a hospital to years after stroke in a community are recommended to provide better chances for early identification of patients at risk because depression and anxiety may manifest at any stage of recovery. Special attention should be given to individuals with culture-bound somatic symptoms in addition to female patients and those who have difficulty swallowing among Korean stroke patients.