Mexico recently declared ambitious goals in reducing domestic CO2 emissions and introduced a carbon tax in 2014. Although negative effects on household welfare and related poverty measures are widely discussed as possible consequences, empirical evidence is missing. We try to fill this gap by simulating an input-output model coupled with household survey data to examine the welfare effects of different carbon tax rates over the income distribution. The currently effective tax rate is small and has negligible effects on household welfare. Higher simulated tax rates, maintaining the current tax base, show a slight progressivity but welfare losses remain moderate. Welfare losses, regressivity and poverty rise more with widening the tax base towards natural gas and the other greenhouse gases methane (CH4) and nitrous oxide (N2O) mainly through food price increases. For a complete analysis of the policy, we simulate a redistribution of calculated tax revenues and find that the resulting effects become highly progressive, also for high rates, wider tax bases and even in the absence of perfect targeting of social welfare programs.