Bread wheat (Triticum aestivum L.) is an important cereal crop that provides >20% of the global calorie intake. Bread wheat contains micronutrients, and thus plays a significant role in nutritional and food securities especially in developing countries. However, its grains are inherently deficient in some micronutrients, particularly iron and zinc, which makes them important biofortification targets. Our objective was to investigate variations in micronutrients and their relationship with grain yield components in wheat under four environments in South Africa. A population of 139 doubled haploid lines derived from a cross between cvv. Tugela-DN and Elands was phenotyped for grain iron and grain zinc concentrations and grain yield components. Heat and drought conditions at Arlington resulted in higher grain zinc concentrations and lower yield component traits; the opposite trend was observed at Bethlehem and Harrismith for both micronutrients and yield components. All traits showed transgressive segregation. Grain iron and zinc concentrations were significantly positively correlated in all four environments. The correlations between these minerals and yield components were inconsistent and ranged from significant to insignificant depending on the environment, indicating that this relationship is non-genetic. The results demonstrate that biofortification of both grain iron and grain zinc can be included as part of the breeding objectives and will not necessarily have adverse relationships with grain yield components.