Burst suppression (BS) is an electroencephalographic state associated with a profound inactivation of the brain. BS and pathological discontinuous electroencephalography (EEG) are often observed in term-age infants with neurological injury and can be indicative of a poor outcome and lifelong disability. Little is known about the neurophysiological mechanisms of BS or how the condition relates to the functional state of the neonatal brain. We used simultaneous EEG and diffuse optical tomography (DOT) to investigate whether bursts of EEG activity in infants with hypoxic ischemic encephalopathy are associated with an observable cerebral hemodynamic response. We were able to identify significant changes in concentration of both oxy and deoxyhemoglobin that are temporally correlated with EEG bursts and present a relatively consistent morphology across six infants. Furthermore, DOT reveals patient-specific spatial distributions of this hemodynamic response that may be indicative of a complex pattern of cortical activation underlying discontinuous EEG activity that is not readily apparent in scalp EEG.