Genome wide association studies (GWAS) are important in discerning the genetic architecture of complex traits such as biomass allocation for improving drought tolerance and carbon sequestration potential of wheat. The objectives of this study were to deduce the population structure and marker-trait association for biomass traits in wheat under drought-stressed and non-stressed conditions. A 100-wheat (Triticum aestivum L.) genotype panel was phenotyped for days to heading (DTH), days to maturity (DTM), shoot biomass (SB), root biomass (RB), root to shoot ratio (RS) and grain yield (GY). The panel was sequenced using 15,600 single nucleotide polymorphism (SNPs) markers and subjected to genetic analysis using the compressed mixed linear model (CMLM) at false discovery rate (FDR < 0.05). Population structure analysis revealed six sub-clusters with high membership ancestry coefficient of ≤0.65 to their assigned sub-clusters. A total of 75 significant marker-trait associations (MTAs) were identified with a linkage disequilibrium threshold of 0.38 at 5cM. Thirty-seven of the MTAs were detected under drought-stressed condition and 48% were on the B genome, where most quantitative trait loci (QTLs) for RB, SB and GY were previously identified. There were seven pleiotropic markers for RB and SB that may facilitate simultaneous selection. Thirty-seven putative candidate genes were mined by gene annotation on the IWGSC RefSeq 1.1. The significant MTAs observed in this study will be useful in devising strategies for marker-assisted breeding for simultaneous improvement of drought tolerance and to enhance C sequestration capacity of wheat.