Sepsis, a dysregulated immune-mediated host response to infection, is the leading cause of morbidity and mortality in critically ill patients. Indices of heart rate variability and complexity (such as entropy) have been proposed as surrogate markers of neuro-immune system dysregulation with diseases such as sepsis. However, these indices only provide an average, one dimensional description of complex neuro-physiological interactions. We propose a novel multiscale network construction and analysis method for multivariate physiological time series, and demonstrate its utility for early prediction of sepsis. We show that features derived from a multiscale heart rate and blood pressure time series network provide approximately 20% improvement in the area under the receiver operating characteristic (AUROC) for four hours ahead prediction of sepsis over traditional indices of heart rate entropy (0.78 versus 0.66). Our results indicate that this improvement is attributable to both the improved network construction method proposed here, as well as the information embedded in the higher order interaction of heart rate and blood pressure time series dynamics. Our final model, which included the most commonly available clinical measurements in patients’ Electronic Medical Records, multiscale entropy features as well as the proposed network-based features, achieved an AUROC of 0.80. Prediction of the onset of sepsis prior to clinical recognition will allow for meaningful earlier interventions (e.g., antibiotic and fluid administration), which have the potential to decrease sepsis-related morbidity, mortality and healthcare costs.