Despite the high prevalence of nurses’ turnover and the turnover intention of new nurses, there are insufficient studies examining turnover intention at the time when job orientation is completed and independent nursing commences. Thus, this study examined turnover intention levels and identified the factors affecting turnover intention of new Generation Z nurses, focusing on job stress and sleep disturbance, at the eighth week after completing job orientation. This was a cross-sectional descriptive correlational study. Using a convenient sampling method, 133 new nurses were recruited. Data were collected using a structured questionnaire consisting of demographic and occupational characteristics, job stress, sleep disturbance, and turnover intention. Descriptive statistics were computed to describe the sample and interest variables. Logistic regression analysis was performed to examine the association of job stress and sleep disturbance with turnover intention. Most nurses were women (91.7%) and approximately two-thirds worked in the surgical ward (n = 61, 45.9%). Turnover intention was 12.8%, average job stress was 40.11 ± 90.7, and average sleep disturbance was 42.39 ± 15.27. New graduate nurses’ turnover intention was associated with job stress (OR = 1.07, 95% CI = 1.02–1.12) and sleep disturbance (OR = 1.19, 95% CI = 1.05–1.35), and this model explained 47.7% of the variance. Study findings determine that job stress and sleep disturbance were significant predictors of turnover intention in new nurses at the eighth week after joining the hospital. Therefore, nursing administrators should focus on new nurses’ job stress and sleep disturbance, and provide them with timely assessment and management to reduce turnover intention.