Inequalities in infant mortality rates (IMRs) are rising in some low- and middle-income countries (LMICs) and decreasing in others, but the explanation for these divergent trends is unclear. We investigate whether government expenditures and redistribution are associated with reductions in inequalities in IMRs. We estimated country-level fixed-effects panel regressions for 48 LMICs (142 country observations). Slope and Relative Indices of Inequality in IMRs (SII and RII) were calculated from Demographic and Health Surveys between 1993 and 2013. RII and SII were regressed on government expenditure (total, health and non-health) and redistribution, controlling for gross domestic product (GDP), private health expenditures, a democracy indicator, country fixed effects and time. Mean SII and RII was 39.12 and 0.69, respectively. In multivariate models, a 1 percentage point increase in total government expenditure (% of GDP) was associated with a decrease in SII of −2.468 [95% confidence intervals (CIs): −4.190, −0.746] and RII of −0.026 (95% CIs: −0.048, −0.004). Lower inequalities were associated with higher non-health government expenditure, but not higher government health expenditure. Associations with inequalities were non-significant for GDP, government redistribution, and private health expenditure. Understanding how non-health government expenditure reduces inequalities in IMR, and why health expenditures may not, will accelerate progress towards the Sustainable Development Goals.