In many agricultural areas, crop production has decreased due to a lack of water availability, which is having a negative impact on sustainability and putting food security at risk. In plants, the plasticity of the root system architecture (RSA) is considered to be a key trait driving the modification of the growth and structure of roots in response to water deficits. The purpose of this study was to examine the plasticity of the RSA traits (mean root diameter, MRD; root volume, RV; root length, RL; and root surface area, SA) associated with drought tolerance in eight Lagenaria siceraria (Mol. Standl) genotypes, representing three different geographical origins: South Africa (BG-58, BG-78, and GC), Asia (Philippines and South Korea), and Chile (Illapel, Chepica, and Osorno). The RSA changes were evaluated at four substrate depths (from 0 to 40 cm). Bottle gourd genotypes were grown in 20 L capacity pots under two contrasting levels of irrigation (well-watered and water-deficit conditions). The results showed that the water productivity (WP) had a significant effect on plasticity values, with the Chilean accessions having the highest values. Furthermore, Illapel and Chepica genotypes presented the highest WP, MRD, and RV values under water-deficit conditions, in which MRD and RV were significant in the deeper layers (20–30 and 30–40 cm). Biplot analysis showed that the Illapel and Chepica genotypes presented a high WP, MRD, and RV, which confirmed that these may be promising drought-tolerant genotypes. Consequently, increased root diameter and volume in bottle gourd may constitute a response to a water deficit. The RSA traits studied here can be used as selection criteria in bottle gourd breeding programs under water-deficit conditions.