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Background/Objectives: Nurses are at high risk for burnout. Identification of biomarkers associated with early manifestations of distress is essential to support effective intervention efforts. Methods: Fifty nurses from a large hospital system participated in a 30-day study of biopsychosocial factors that may contribute to burnout. Nurses wore an Oura ring that collected behavioral data and they completed a self-report burnout questionnaire at baseline and the end of the study period. Machine learning models were developed to evaluate whether objective measures could predict burnout states and changes at the end of the study period. Analyses were exploratory and hypothesis-generating for future work. Results: Data for 45 participants were included in the analyses. Participants with burnout had significantly higher sleep variability. Sleep measures provided 75.75% accuracy in ability to discriminate between burnout states. Heart rate-based measures better modeled changes in symptomatic components of burnout (Emotional Exhaustion, Depersonalization) over time. Heart rate-based measures provided a R-squared value of 0.13 (p < 0.05) (RMSE of 7.41) in a regression model of changes in Emotional Exhaustion evaluated in a leave-one-participant-out cross-validation. Conclusions: Sleep measures’ association with a state of burnout may reflect the longer-term manifestations of chronic exposure to workplace stress. Short-term changes in burnout symptoms are associated with disturbances in heart rate measures. Wearable technology may support monitoring/early identification of those at risk for burnout.