Background/Objectives: Foot arch status and muscular strength may influence balance and physical performance. However, evidence regarding their associations with unilateral balance performance, walking performance, and lower limb functional capacity in healthy young adults, particularly in Saudi Arabia, remains limited. This study investigated the associations of foot arch status and handgrip strength with these outcomes in healthy young Saudi adults. Methods: In this cross-sectional study, 104 healthy young adults (mean age: 21.1 ± 1.2 years; 52.9% female) underwent assessment of foot arch status using the sit-to-stand navicular drop test (SSNDT) and of muscular strength using a digital hand dynamometer. Unilateral balance performance was assessed using the single-leg stance test (SLST) under eyes open and eyes closed conditions. Walking performance and lower limb functional capacity were assessed using the 10 m walk test (10-MWT) and the 30 s chair stand test (30 s-CST), respectively. Generalised estimating equations and multivariable linear regression models were used to examine adjusted associations. Results: Greater SSNDT scores were independently associated with shorter SLST duration for both the right (β = −0.46, p = 0.003) and left feet (β = −0.25, p = 0.048). Greater handgrip strength was independently associated with longer SLST duration for the right foot only (β = 0.17, p = 0.019). Neither SSNDT score nor handgrip strength was independently associated with 10-MWT or 30 s-CST outcomes after adjustment. Athletic participants demonstrated superior balance and chair-stand performance, while the male sex was associated with longer SLST duration. Conclusions: Greater functional lowering of the medial longitudinal arch was independently associated with poorer unilateral balance performance, whereas handgrip strength demonstrated a more limited association. These findings suggest that foot arch behaviour is more strongly related to balance performance than to walking performance or lower limb functional capacity.