The bidirectional interaction between undernutrition and infection can be devastating to child health. Nutritional deficiencies stunt growth, impair immunity, increase susceptibility to both infection and more severe outcomes from common infections. Simultaneously, infections compound undernutrition by increasing metabolic demand, reducing food intake, and impairing nutrient absorption. Treatment of acute malnutrition (wasting) can reverse at least some of its deleterious effects and reduce susceptibility to, and transmission of, 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 of children aged 6-23 months old, stratified by 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 reduce susceptibility to measles-related death and to increase engagement with the health sector, leading to increased vaccination rates. We found that if all wasted children receive therapeutic feeding, and if this leads to an increase in measles vaccination uptake, up to 12%, 20%, and 23% reductions in measles infections, measles-attributable mortality, and overall mortality among wasted children, respectively, could be averted. 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 a 64-66% reduction in measles infection and mortality and 27% 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 in order to improve child survival beyond what would be expected from the additive benefits of each intervention.