(1) Background: The countermovement jump (CMJ) on a force plate could be a sensitive assessment for detecting early lower-limb muscle mechanical deficits in the early stages of multiple sclerosis (MS). CMJ performance is known to be influenced by various anthropometric, physiological, and biomechanical factors, mostly investigated in children and adult athletes. Our aim was to investigate the association of age, sex, and BMI with muscle mechanical function using CMJ to provide a comprehensive overview of lower-limb motor function in people with multiple sclerosis (pwMS). (2) Methods: A cross-sectional study was conducted with pwMS (N = 164) and healthy controls (N = 98). All participants performed three maximal CMJs on a force plate. Age, sex, and BMI were collected from all participants. (3) Results: Significant age, sex, and BMI effects were found for all performance parameters, flight time, and negative and positive power for pwMS and HC, but no significant interaction effects with the group (pwMS, HC) were detected. The highest significant effects were found for sex on flight time (η2 = 0.23), jump height (η2 = 0.23), and positive power (η2 = 0.13). PwMS showed significantly lower CMJ performance compared to HC in middle-aged (31-49 years), with normal weight to overweight and in both women and men. (4) Conclusions: This study showed that age, sex, and BMI are associated with muscle mechanical function in pwMS and HC. These results may be useful in developing reference values for CMJ. This is a crucial step in integrating CMJ into the diagnostic assessment of people with early MS and developing individualized and effective neurorehabilitative therapy.