The health burden of anthropogenic climate change is growing exponentially, but present-day impacts remain difficult to measure. Here, we leverage a recently-published comprehensive dataset of 50,425 population surveys to investigate whether human-caused climate change has increased the burden of childhood malaria across sub-Saharan Africa. In historical data, we find that prevalence shows a robust response to temperature and extreme precipitation, consistent with expectations from previous empirical and epidemiological work. Comparing historical climate reconstructions to counterfactual simulations without anthropogenic warming, we find two-to-one odds that human-caused climate change has increased the overall prevalence of childhood malaria across sub-Saharan Africa since 1901. We estimate that by 2014, human-caused climate change was responsible for an average of 84 excess cases of malaria per 100,000 children ages 2 to 10, with higher elevation and cooler regions in southern and east Africa having greater increases. Under future climate change, we project increasing temperatures could plausibly accelerate the eradication of malaria in west and central Africa, where the present-day burden is highest, leading to continent-wide average reductions of 89 (low greenhouse gas emissions, SSP1-RCP2.6) to 1,750 (high emissions, SSP5-RCP8.5) cases per 100,000 children by the end of the century. However, we find that limiting future global warming to below 2 degrees C (SSP1-RCP2.6) compared to ~3 degrees C (SSP2-RCP4.5) could prevent an average of 496 excess cases in southern Africa, and 40 excess cases in east Africa, per 100,000 children by 2100. Our study resolves a decades-old debate about one of the earliest health impacts of global warming, and provides a template for future work measuring the true global burden of climate change.