Deficiency of metals, primarily Fe and Zn, affects over half of the world’s population. Human diets dominated by cereal products cause micronutrient malnutrition, which is common in many developing countries where populations depend heavily on staple grain crops such as wheat, maize, and rice. Biofortification is one of the most effective approaches to alleviate malnutrition. Genetically stable mutant spring wheat lines (M7 generation) produced via 100 or 200 Gy gamma treatments to broaden genetic variation for grain nutrients were analyzed for nutritionally important minerals (Ca, Fe, and Zn), their bioavailability, and grain protein content (GPC). Variation was 172.3–883.0 mg/kg for Ca, 40.9–89.0 mg/kg for Fe, and 22.2–89.6 mg/kg for Zn. In mutant lines, among the investigated minerals, the highest increases in concentrations were observed in Fe, Zn, and Ca when compared to the parental cultivar Zhenis. Some mutant lines, mostly in the 100 Gy-derived germplasm, had more than two-fold higher Fe, Zn, and Ca concentrations, lower phytic acid concentration (1.4–2.1-fold), and 6.5–7% higher grain protein content compared to the parent. Variation was detected for the molar ratios of Ca:Phy, Phy:Fe, and Phy:Zn (1.27–10.41, 1.40–5.32, and 1.78–11.78, respectively). The results of this study show how genetic variation generated through radiation can be useful to achieve nutrient biofortification of crops to overcome human malnutrition.