Livestock provides an additional source of income for marginal cropping farmers, but crop residues that are used as a main source of animal feed are characteristically low in digestibility and protein content. This reduces the potential livestock product yield and quality. The key trait, which influences the quality and the cost of animal feed, is digestibility. In this study, we demonstrate that sorghum breeding can be directed to achieve genetic gains for both fodder biomass and digestibility without any trade-offs. The genotypic variance has shown significant differences for biomass across years (13,035 in 2016 and 3,395 in 2017) while in vitro organic matter digestibility (IVOMD) showed significant genotypic variation in 2016 (0.253) under drought. A range of agronomic and fodder quality traits was found to vary significantly in the population within both the control and drought conditions and across both years of the study. There was significant genotypic variance (σg2) and genotypic × treatment variance (σgxt2) in dry matter production in a recombinant inbred line (RIL) population in both study years, while there was only significant σg2 and σgxt2 in IVOMD under the control conditions. There was no significant correlation identified between biomass and digestibility traits under the control conditions, but there was a positive correlation under drought. However, a negative relation was observed between digestibility and grain yield under the control conditions, while there was no significant correlation under drought population, which was genotyped using the genotyping-by-sequencing (GBS) technique, and 1,141 informative single nucleotide polymorphism (SNP) markers were identified. A linkage map was constructed, and a total of 294 quantitative trait loci (QTLs) were detected, with 534 epistatic interactions, across all of the traits under study. QTL for the agronomic traits fresh and dry weight, together with plant height, mapped on to the linkage group (LG) 7, while QTL for IVOMD mapped on to LG1, 2, and 8. A number of genes previously reported to play a role in nitrogen metabolism and cell wall-related functions were found to be associated with these QTL.