Recent studies with Nile tilapia have shown divergent results regarding the possibility of selecting on morphometric measurements to promote indirect genetic gains in fillet yield (FY). The use of indirect selection for fillet traits is important as these traits are only measurable after harvesting. Random regression models are a powerful tool in association studies to identify the best time point to measure and select animals. Random regression models can also be applied in a multiple trait approach to analyze indirect response to selection, which would avoid the need to sacrifice candidate fish. Therefore, the aim of this study was to investigate the genetic relationships between several body measurements, weight and fillet traits throughout the growth period and to evaluate the possibility of indirect selection for fillet traits in Nile tilapia. Data were collected from 2042 fish and was divided into two subsets. The first subset was used to estimate genetic parameters, including the permanent environmental effect for BW and body measurements (8758 records for each body measurement, as each fish was individually weighed and measured a maximum of six times). The second subset (2042 records for each trait) was used to estimate genetic correlations and heritabilities, which enabled the calculation of correlated response efficiencies between body measurements and the fillet traits. Heritability estimates across ages ranged from 0.05 to 0.5 for height, 0.02 to 0.48 for corrected length (CL), 0.05 to 0.68 for width, 0.08 to 0.57 for fillet weight (FW) and 0.12 to 0.42 for FY. All genetic correlation estimates between body measurements and FW were positive and strong (0.64 to 0.98). The estimates of genetic correlation between body measurements and FY were positive (except for CL at some ages), but weak to moderate (−0.08 to 0.68). These estimates resulted in strong and favorable correlated response efficiencies for FW and positive, but moderate for FY. These results indicate the possibility of achieving indirect genetic gains for FW and by selecting for morphometric traits, but low efficiency for FY when compared with direct selection.