Background Dietary mineral deficiencies are widespread globally causing a large disease burden. However, estimates of deficiency prevalence are often only available at national scales or for small population sub-groups with limited relevance for policy makers. Methods This study combines food supply data from the Third Integrated Household Survey of Malawi with locally-generated food crop composition data to derive estimates of dietary mineral supplies and prevalence of inadequate intakes in Malawi. Results We estimate that >50 % of households in Malawi are at risk of energy, calcium (Ca), selenium (Se) and/or zinc (Zn) deficiencies due to inadequate dietary supplies, but supplies of iron (Fe), copper (Cu) and magnesium (Mg) are adequate for >80 % of households. Adequacy of iodine (I) is contingent on the use of iodised salt with <1 % of households getting adequate I supply from food alone. Hidden hunger is likely to be widespread: among households with adequate energy supply, 30, 56 and 27 % had inadequate supplies of Ca, Se and Zn, respectively. Over 80 % of the poorest households had inadequate dietary supplies of Ca and Zn compared to <30 % of the wealthiest households; >80 % of rural households living on low-pH soils had inadequate dietary Se supplies compared to 55 % on calcareous soils; concurrent inadequate supplies of Ca, Se and Zn were observed in >80 % of the poorest rural households living in areas with non-calcareous soils. Prevalence of inadequate dietary supplies was greater in rural than urban households for all nutrients except Fe. Interventions to address dietary mineral deficiencies were assessed. For example, an agronomic biofortification strategy could reduce the prevalence of inadequate dietary Se supplies from 82 to 14 % of households living in areas with low-pH soils, including from 95 to 21 % for the poorest subset of those households. If currently-used fertiliser alone were enriched with Se then the prevalence of inadequate supplies would fall from 82 to 57 % with a cost per alleviated case of dietary Se deficiency of ~ US$ 0.36 year−1. Conclusions Household surveys can provide useful insights into the prevalence and underlying causes of dietary mineral deficiencies, allowing disaggregation by spatial and socioeconomic criteria. Furthermore, impacts of potential interventions can be modelled.