(1) Background: Neonatal brain injury can lead to permanent neurodevelopmental impairments. Notably, suppressing inflammatory pathways may reduce damage. To determine the role of neuroinflammation in the progression of neonatal brain injury, we investigated the effect of treating neonatal rat pups with the immunosuppressant tacrolimus at two time points: before and after hypoxic–ischaemic (HI)-induced injury. (2) Methods: To induce HI injury, postnatal day (PND) 10 rat pups underwent single carotid artery ligation followed by hypoxia (8% oxygen, 90 min). Pups received daily tacrolimus (or a vehicle) starting either 3 days before HI on PND 7 (pre-HI), or 12 h after HI (post-HI). Four doses were tested: 0.025, 0.05, 0.1 or 0.25 mg/kg/day. Pups were euthanised at PND 17 or PND 50. (3) Results: All tacrolimus doses administered pre-HI significantly reduced brain infarct size and neuronal loss, increased the number of resting microglia and reduced cellular apoptosis (p < 0.05 compared to control). In contrast, only the highest dose of tacrolimus administered post-HI (0.25 mg/kg/day) reduced brain infarct size (p < 0.05). All doses of tacrolimus reduced pup weight compared to the controls. (4) Conclusions: Tacrolimus administration 3 days pre-HI was neuroprotective, likely mediated through neuroinflammatory and cell death pathways. Tacrolimus post-HI may have limited capacity to reduce brain injury, with higher doses increasing rat pup mortality. This work highlights the benefits of targeting neuroinflammation during the acute injurious period. More specific targeting of neuroinflammation, e.g., via T-cells, warrants further investigation.