Fat mass and fat-free mass have become useful clinical indices in determining healthy growth and physical development during critical periods of childhood and adolescence; however, despite a wide range of nutritional surveillance its study is limited by a lack of reference data. The purpose of this study was to establish sex-specific and age-specific standards for fat mass and fat-free mass in a large sample of Croatian children and adolescents. In this cross-sectional study, we collected data from 12,678 participants aged 11 to 18 years old (mean age ± standard deviation (SD): 14.17 ± 2.25 years; height 164.56 ± 11.31 cm; weight: 57.45 ± 13.73 kg; body mass index: 21.24 ± 3.67 kg/m2; 53% girls). Fat mass and fat-free mass were measured three times by bioelectrical impedance. The Lambda, Mu and Sigma methods were used to create percentile charts for fat mass index (FMI) and fat-free mass index (FFMI; fat mass and fat-free mass divided by height2). Sex and age differences were calculated using an analysis of variance (ANOVA) with post hoc comparisons. Boys had lower FMI (from 2.66 to 3.89) and higher FFMI values (from 16.90 to 17.80) in all age groups, compared to girls (for FMI from 2.79 to 5.17 and for FFMI from 14.50 to 14.90, p < 0.001). In boys, FMI slightly declined until the age of 14, after which an increase from the age of 15 to 18 was observed. In girls, FMI gradually increased from the age of 11 to 18 (p < 0.001). In general, FFMI increased by age in boys [F(7,5440) = 52.674, p < 0.001], while girls had more stable FFMI across all age groups [F(7,7222) = 2.728, p = 0.057]. The newly established sex-specific and age-specific reference data could be used for national surveillance and to screen for children and adolescents with high FMI and low FFMI.