Heritability and genetic correlations for body weight at harvest size (BW), grow‐out survival (SU), and log‐transformed infectious hypodermal and hematopoietic necrosis virus (IHHNV) load (VLln) in Litopenaeus vannamei were estimated. Data were obtained in 2012 from a shrimp breeding population in Mexico using 12,440 shrimp for BW and 16,814 shrimp for SU, and quantitative polymerase chain reaction determinations from 160 full‐sib families were obtained for VLln. DNA was extracted from pooled muscle samples of six shrimp per family for a total of 960 individuals. Heritability estimates for BW, SU, and VLln at the family mean and at individual levels were 0.24 ± 0.08, 0.02 ± 0.01, 0.42 ± 0.45, and 0.08 ± 0.11, respectively. Genetic correlation estimates of BW with SU, BW with VLln, and VLln with SU were 0.40, −0.04, and −0.57, respectively. Our results suggest that VLln has genetic variation and a favorable genetic association with BW and SU. No serious drawbacks were found from selection responses estimated using single‐trait and multitrait indices to increase BW and SU and decrease VLln. Favorable correlated responses for IHHNV tolerance estimated as BW/VLln and SU/VLln were also found. This study offers new insights into the possibility of using IHHNV viral load as a possible selection criterion in L. vannamei breeding programs.