Background Body mass index (BMI) is an important indicator of overweight and obesity. Unlike BMI, body fat percentage (BF%) can be utilized to estimate body composition regardless of weight and height. The association between BMI and BF%, as well as the impact of age and gender, may help estimate the prevalence of obesity more clearly. This study aimed to assess the relationship between BMI and BF%, examine the effect of age and gender on this relationship, and establish the linearity/curvilinearity of this relationship. Methodology The body composition analysis of 1,150 participants in various institutional events (institution foundation day) during 2019 and 2023 was performed using the Accuniq bio-electrical impedance analyzer (BIA) (Accuniq, Netherlands). The participants included undergraduate, postgraduate medical, and PhD students, as well as employees of All India Institute of Medical Sciences, New Delhi. Age groups were categorized as under 17 years, young adults (18-25 years), adults (26-44 years), middle-aged adults (45-59 years), and older adults (≥60 years). Pearson's correlation coefficient (r) was used for analyzing the relationship between BMI and BF%. To assess the effect of age and gender on this relationship, multiple regression analysis was applied, and polynomial regression was applied to test its linearity. The data were analyzed using SPSS version 25 (IBM Corp., Armonk, NY, USA). Results Males made up a larger proportion of the participants (56.3%; 647). The mean age of the participants was 36.5 ± 13.6 years. The mean BMI and BF% were 24.7 ± 4.0 kg/m2 and 29.1 ± 8.7%, respectively. A significant and moderate positive correlation (r = 0.630, p < 0.01) was observed between BMI and BF%. The mean ± SD of BMI and BF% had a directly proportional relationship with age. Among both genders, females showed a greater correlation (r = 0.852). Both age and gender had a significant effect on this relationship, with gender impacting more than age (ß = 0.488, p < 0.000). The curvilinear nature of the relationship between BMI and BF% was demonstrated with the female model showing a more precise fit (R2 = 0.72, standard error of the estimate = 3.3%). Conclusions The relationship between BMI and BF% was significant and positive in this group of Indians. This relationship was significantly impacted by age and gender and was curvilinear in nature. Females had a higher association than males between BMI and BF%. The study suggests that BMI, BF%, and the effects of age and gender should be taken into consideration when predicting obesity.