This paper advances previous literature that has posited a climate-nutrition link without identifying a specific pathway via agriculture. We measure the specific effects of exposure to extreme heat on maize yields in Tanzania, and then test whether prenatal heat-induced yield losses predict subsequent child growth outcomes. In the first stage we find that substituting one full day (24 h) exposure to 39 °C for a day at 29 degrees reduces predicted yield for the entire growing season by 6–11%. In the second stage we find that in utero exposure to growing degree days greater than 29 °C predicts lower postnatal HAZ scores for Tanzanian boys 0–5 years of age, but not girls. Consistent with a maternal malnutrition mechanism, we also find a negative association between maize yields and women’s body mass. Insofar as climate change is likely to increase the incidence of heat shocks in much of sub-Saharan Africa, our results suggest a significant risk of adverse nutritional impacts.