Understanding the impact of changes in climatic variables on reference evapotranspiration (ETo) is important for predicting possible implications of climate change on the overall hydrology of an area. This study aimed to determine the effects of changes in ETo with respect to changes in climatic variables. In addition, the specific objective was to determine the sensitivity coefficients of ETo in seven different locations in Nigeria with distinct agroecology, namely Maiduguri (Sahel savannah), Sokoto (Sudan savannah), Kaduna (Guinea savannah), Jos (Montane), Enugu (Derived Savannah), Ibadan (tropical rainforest), and Port Harcourt (coastal). The results showed that ETo is most sensitive to changes in maximum temperature (Tmax) in Maiduguri, Sokoto, Kaduna, and Jos. In Enugu and Ibadan, ETo is most sensitive to changes in solar radiation (Rs), while in Port Harcourt, ETo is most sensitive to relative humidity (RH). Overall, based on the average annual sensitivity coefficients (SCs) of the study area, the SC is ranked in the order: RH > Rs > Tmax > U2 > Tmin. Also, the results showed positive SCs of ETo to Rs, Tmax, U2, Tmin, and negative SC for RH. This study can serve as a baseline for sustainable water management in the context of climate change and adapted to areas with a similar climate.