Background: Nigeria’s neonatal mortality rate (NMR) and under-five mortality rate (U5MR) are 39 per 1,000 and 120 per 1,000 live births, respectively. On average, 0.23 million neonates and 0.7 million under-five children die every year, but some states contribute more to this burden than others. If the country is to meet its sustainable development goal (SDG) targets for NMR and U5MR, it needs to make progress at both the national and subnational levels. Methods: Using the 2016-2017 Nigeria Multiple Indicator Cluster Survey (MICS), we estimated state-level neonatal and under-five mortality rates. Next, we estimated how long it would take for each state to reach the SDG targets for NMR and U5MR. Finally, we estimated the average number of neonatal and under-five deaths that could be averted between 2018 and 2030 in each state under different scenarios. Results: At current average annual rates of decline, Nigeria is unlikely to meet both sustainable development goals targets for NMR and U5MR. At the subnational level, some states are close to or have met both NMR and U5MR targets, while others are projected to meet the targets as late as 2088 (58 years delayed). Between 850,000 and 1.89 million neonatal deaths could be averted between 2018 and 2030, while 3.1 million to 5.96 million under-five deaths could be averted over the same period. Conclusions: Nigeria has the potential to achieve its SDG targets for NMR and U5MR, and in the process avert millions of preventable child deaths. But this will not happen under a business-as-usual approach. The NMR and U5MR trajectories achieved by high-performing states is evidence that achieving these SDG targets is possible. For the country to achieve positive results nationally, systems that encourage peer learning and transfer of technical expertise between states are needed.