Mung bean [Vigna radiata (L.) Wilczek] is a drought-tolerant, short-duration crop, and a rich source of protein and other valuable minerals, vitamins, and antioxidants. The main objectives of this research were (1) to study the root traits related with the phenotypic and genetic diversity of 375 mung bean genotypes of the Iowa (IA) diversity panel and (2) to conduct genome-wide association studies of root-related traits using the Automated Root Image Analysis (ARIA) software. We collected over 9,000 digital images at three-time points (days 12, 15, and 18 after germination). A broad sense heritability for days 15 (0.22–0.73) and 18 (0.23–0.87) was higher than that for day 12 (0.24–0.51). We also reported root ideotype classification, i.e., PI425425 (India), PI425045 (Philippines), PI425551 (Korea), PI264686 (Philippines), and PI425085 (Sri Lanka) that emerged as the top five in the topsoil foraging category, while PI425594 (unknown origin), PI425599 (Thailand), PI425610 (Afghanistan), PI425485 (India), and AVMU0201 (Taiwan) were top five in the drought-tolerant and nutrient uptake “steep, cheap, and deep” ideotype. We identified promising genotypes that can help diversify the gene pool of mung bean breeding stocks and will be useful for further field testing. Using association studies, we identified markers showing significant associations with the lateral root angle (LRA) on chromosomes 2, 6, 7, and 11, length distribution (LED) on chromosome 8, and total root length-growth rate (TRL_GR), volume (VOL), and total dry weight (TDW) on chromosomes 3 and 5. We discussed genes that are potential candidates from these regions. We reported beta-galactosidase 3 associated with the LRA, which has previously been implicated in the adventitious root development via transcriptomic studies in mung bean. Results from this work on the phenotypic characterization, root-based ideotype categories, and significant molecular markers associated with important traits will be useful for the marker-assisted selection and mung bean improvement through breeding.