Measles is a major cause of childhood morbidity and mortality in many parts of the world. Estimates of the case-fatality rate (CFR) of measles have varied widely from place to place, as well as in the same location over time. Amongst populations that have experienced famine or armed conflict, measles CFR can be especially high, although past work has mostly focused on refugee populations. Here, we estimate measles CFR between 1970 and 1991 in a rural region of Bangladesh, which experienced civil war and famine in the 1970s. We use historical measles mortality data and a mechanistic model of measles transmission to estimate the CFR of measles. We first demonstrate the ability of this model to recover the CFR in the absence of incidence data, using simulated mortality data. Our method produces CFR estimates that correspond closely to independent estimates from surveillance data, and we can capture both the magnitude and the change in CFR suggested by these previous estimates. We use this method to quantify the sharp increase in CFR that resulted in the large number of deaths during a measles outbreak in the region in 1976. Most of the children who died during this outbreak were born during a famine in 1974, or in the two years preceding the famine. Our results suggest that the period of turmoil during and after the 1971 war, and the sustained effects of the famine, is likely to have contributed to the high fatality burden of the 1976 measles outbreak in Matlab.