Micronutrient deficiency is a widespread food-related health problem around the world. The present study was conducted to evaluate a set of 63 advanced breeding lines of bread wheat (Triticum aestivum L.) for grain iron (GFe) and grain zinc (GZn) concentrations, and to characterise the germplasm set via simple sequence repeat (SSR) markers (both genic and random). Substantial variation was found for both micronutrients. GFe concentration ranged from 28.9 to 67.4 mg kg^–1 and GZn from 26.3 to 56.6 mg kg^–1. Molecular characterisation with six genic and 20 random SSR markers detected 168 alleles with an average of 3.170 alleles per locus. Analysis of genotypic data based on division into two subpopulations revealed 165 alleles with an average of 3.113 alleles per locus in the low GFe–GZn subpopulation, whereas in the high GFe–GZn subpopulation, 149 alleles with an average of 2.811 alleles per locus were detected. Genic SSRs detected a higher average number of alleles (3.273 alleles per locus) than random SSRs (3.143 alleles per locus). Hierarchical clustering using genic markers alone clustered the whole germplasm set into two distinct groups: one possessing low GFe–GZn genotypes, the other with high GFe–GZn genotypes. Study of marker–trait associations (MTAs) identified seven new MTAs (six for GZn and one for GFe) and validated one MTA for GZn concentration. The promising genotypes and MTAs identified during the study will prove useful in wheat bio-fortification programs in the future.