[Purpose] This study aimed to analyze the prevalence of hypertension according to the body mass index (BMI) and relative handgrip strength (RHGS) among elderly individuals in Korea. [Methods] We analyzed the data of 44,183 Korean elderly individuals over 65 years old (men: n = 15,798, age = 73.31 ± 5.04 years, women: n = 28,385, age = 72.14 ± 5.04 years) obtained from the Korean National Fitness Assessment in 2019. All the participants were categorized into three groups according to the BMI and RHGS; additionally, one-way ANOVA and logistic regression analysis were performed. [Results] Overweight (men: 1.16 odds ratio [OR] 1.06–1.26, 95% confidence interval [CI]; women: 1.15 OR, 1.07–1.23 95% CI) and obese (men: 1.54 OR, 1.42–1.66 95% CI; women: 1.44 OR, 1.36–1.53 95% CI) elderly individuals showed a higher prevalence of hypertension than elderly individuals with normal weight, after controlling for age. In men, a lower RHGS was associated with a higher prevalence of hypertension after controlling for age (weak RHGS: 1.09 OR, 1.00–1.17 95% CI; middle RHGS: 1.21 OR, 1.12–1.31 95% CI vs. strong RHGS). [Conclusion] A higher BMI was associated with the prevalence of hypertension in the elderly Korean population. In addition, a lower RHGS was associated with the prevalence of hypertension in elderly Korean men.