Sorghum biofortification is a cost-effective approach to solving the issue of micronutrient deficiencies in human diets. Research programs face challenges, e.g., phenotyping time, cost, and accuracy in evaluating breeding populations across years and environments, which can be addressed through genomic selection (GS). The present GS work on sorghum grain Fe and Zn contents revealed that the multi-trait genomic best linear unbiased prediction (GBLUP) model (MT-GBLUP) consistently outperformed single-trait GBLUP (ST-GBLUP) in terms of prediction accuracy (PA) under different breeding resource-constrained scenarios. The PA gain by MT-GBLUP for Fe (0.274) and Zn (0.183) was greater when information was borrowed from auxiliary agronomic traits evaluated in a few locations than when only highly correlated target traits (Fe and Zn) were evaluated in more years and locations (PA gain ≤ 0.005). These results suggest that easily scorable non-target traits can inform and improve MT-GBLUP prediction accuracy for the genomic estimated breeding values of the target traits, thereby significantly saving multi-environment testing resources and potentially boosting genetic gain per unit time and cost.