The oil price -inflation relationship has continued to significantly feature in the macroeconomic debate, a situation that is guaranteed by nineteen oil market disruptions experienced by the world over the last 40 years (Verleger, 2019). The debate on the dynamic behavior between oil price and domestic inflation is an ongoing process and recent literature indicated that the relationship shows non-linearities, which could have some implication for monetary policymaking. We estimate NARDL models of the link between oil price and inflation decomposed into consumer price index sub-indices of food, core, other energy and transport and find support for long-run asymmetry in relation to oil price shocks as well as incomplete pass-through of oil price to inflation. Our results suggest that it takes within 4-8 quarters for the disaggregated inflation to converge to its long-run equilibrium after a negative or positive unitary oil price shock. Hence, we conclude that there is the need to boost domestic oil refining capacity and fostering of competition in the domestic market as well as unlocking investment in other bio-fuels and other low-cost energy products to reduce energy imports in Nigeria.