The bidirectional interaction between undernutrition and infection can be devastating to child health. Nutritional deficiencies impair immunity and increase susceptibility to infection. Simultaneously, infections compound undernutrition by increasing metabolic demand and impairing nutrient absorption. Treatment of acute malnutrition (wasting) can reverse some of its deleterious effects and reduce susceptibility to infectious diseases. Nutrition-specific approaches may be packaged with other interventions, including immunization, to support overall child health. To understand how mass nutritional supplementation, treatment of wasting, and vaccination affect the dynamics of a vaccine-preventable infection, we developed a population-level, compartmental model of measles transmission stratified by age and nutrition status. We simulated a range of scenarios to assess the potential reductions in measles infection and mortality associated with targeted therapeutic feeding for children who are wasted and with a mass supplementation intervention. Nutrition interventions were assumed to increase engagement with the health sector, leading to increased vaccination rates. We found that the combination of wasting treatment and mass supplementation coverage followed by an increase in vaccination coverage of non-wasted children from a baseline of 75% to 85%, leads to 34% to 57% and 65% to 77% reduction in measles infection and mortality and 56% to 60% reduction in overall mortality among wasted children, compared with the wasting treatment alone. Our work highlights the synergistic benefits that may be achieved by leveraging mass nutritional supplementation as a touch point with the health system to increase rates of vaccination and improve child survival beyond what would be expected from the additive benefits of each intervention.