Little is known about the relationship between health-related physical fitness factors and obesity-related factors in individuals with intellectual disabilities. We investigated the prevalence of obesity and the relationship between obesity-related factors and health-related physical fitness factors among people with intellectual disabilities in South Korea to identify the physical fitness factors that influence the degree of obesity. For obesity-related factors, we measured body composition (height, weight, body mass index—BMI, and body fat percentage) of 108 subjects with intellectual disabilities (mean ± standard deviation; age = 24.4 ± 8.45 years). For health-related physical fitness factors, we measured muscular strength, muscular endurance, and flexibility. There was a significant negative correlation between muscular endurance and obesity factors (BMI, r = −0.306, p < 0.01; body fat percentage, r = −0.402, p < 0.01). Further, the prevalence of obesity (34.3%) and being overweight (17.6%) among people with intellectual disabilities was high in South Korea. In addition, muscular endurance was found to have a significant effect on the obesity level (β = −0.239, p < 0.000). This suggests that a program that considers muscular endurance should be prioritized when implementing an exercise intervention strategy for the treatment of overweight and obesity among people with intellectual disabilities.