Roots are essential organs for a plant’s ability to absorb water and obtain mineral nutrients, hence they are critical to its development. Plants use root architectural alterations to improve their chances of absorbing nutrients when their supply is low. Nine root traits of a Brassica napus association panel were explored in hydroponic-system studies under low potassium (K) stress to unravel the genetic basis of root growth in rapeseed. The quantitative trait loci (QTL) and candidate genes for root development were discovered using a multilocus genome-wide association study (ML-GWAS). For the nine traits, a total of 453 significant associated single-nucleotide polymorphism (SNP) loci were discovered, which were then integrated into 206 QTL clusters. There were 45 pleiotropic clusters, and qRTA04-4 and qRTC04-7 were linked to TRL, TSA, and TRV at the same time, contributing 5.25–11.48% of the phenotypic variance explained (PVE) to the root traits. Additionally, 1360 annotated genes were discovered by examining genomic regions within 100 kb upstream and downstream of lead SNPs within the 45 loci. Thirty-five genes were identified as possibly regulating root-system development. As per protein–protein interaction analyses, homologs of three genes (BnaC08g29120D, BnaA07g10150D, and BnaC04g45700D) have been shown to influence root growth in earlier investigations. The QTL clusters and candidate genes identified in this work will help us better understand the genetics of root growth traits and could be employed in marker-assisted breeding for rapeseed adaptable to various conditions with low K levels.