The aim of this study was to evaluate the genetic parameters of several breast meat quality traits and their genetic relationships with some slaughter traits [BW, breast yield (BRY), and abdominal fat yield (AFY)]. In total, 1,093 pedigreed quail were slaughtered at 35 d of age to measure BRY, AFY, and breast meat quality traits [ultimate pH (pHU), Commission Internationale d'Eclairage color parameters (L*, lightness; a*, redness; and b*, yellowness), thawing and cooking loss (TL and CL, respectively), and Warner-Bratzler shear value (WB)]. The average pHU, L*, a*, and b* were determined to be 5.94, 43.09, 19.24, and 7.74, respectively. In addition, a very high WB average (7.75 kg) indicated the firmness of breast meat. High heritabilities were estimated for BW, BRY, and AFY (0.51, 0.49, and 0.35). Genetic correlations of BW between BRY and AFY were found to be high (0.32 and 0.58). On the other hand, the moderate negative relationship between BRY and AFY (-0.24) implies that selection for breast yield should not increase abdominal fat. The pHU was found to be the most heritable trait (0.64), whereas the other meat quality traits showed heritabilities in the range of 0.39 to 0.48. Contrary to chickens, the genetic correlation between pHU and L* was low. The pHU exhibited a negative and high correlation with BW and AFY, whereas L* showed a positive but smaller relationship with these traits. Moreover, pHU exhibited high negative correlations (-0.43 and -0.62) with TL and WB, whereas L* showed a moderate relationship (0.24) with CL. This genetic study confirmed that the multi-trait selection could be used to improve meat quality traits. Further, the ultimate pH of breast meat is a relevant selection criterion due to its strong relationships with either water-holding capacity and texture or low abdominal fatness.