This study analyzes the nexus of electricity infrastructure investment (EII), rural household income, and household carbon emissions (HCEs) using panel data from China's 30 provinces from 2003 to 2020. Firstly, we consider the impact of EII on the direct HCEs (DHCEs) caused by the direct consumption of fossil fuels and investigate the mediating effect of income level and income variance. The empirical results show that the growth of EII reduces rural DHCEs through the transmission channels of income level, whereas income variance limits the negative relationship between EII and DHCEs. Then, we estimate the emissions embodied in household expenditure on goods and services of different income groups, that is, indirect HCEs (IHCEs), and develop a counterfactual scenario to assess the effects of EII on the total HCEs (the sum of DHCEs and IHCEs) in 2017. The scenario analysis indicates that without increased EII in 2017, the total national HCEs would increase by 0.9%, mainly due to the increased per capita HCEs of low-income groups (+11.6%). Besides, the total HCEs in ten provinces are influenced significantly by the change of income distribution driven by the change of EII, with Guangdong experiencing the largest decrease of HCEs (2.6 Mt) due to the movements of residents from the lower-income group to the lowest-income group. Thus, there is a trade-off between HCE reduction and poverty alleviation when developing EII in rural China.