The rennet-induced coagulation ability of milk is important in cheese production. For Swedish Red Dairy Cattle (RDC), this ability is reduced because of a high prevalence of noncoagulating (NC) milk. In this study, we simultaneously combined genetic parameters for NC milk, milk coagulation properties, milk composition, physical traits, and milk protein composition. Our aim was to estimate heritability and genetic and phenotypic correlations for NC milk and 24 traits (milk coagulation properties, milk composition, physical traits, and milk protein composition). Phenotypes and ~7,000 SNP genotypes were available for all 600 Swedish RDC. The genotypes were imputed from ~7,000 SNP to 50,000 SNP. Variance components and genetic parameters were estimated with an animal model. In Swedish RDC, a moderate heritability estimate of 0.28 was found for NC milk. For the other 24 traits, heritability estimates ranged from 0.12 to 0.77 (standard errors from 0.08 to 0.18). A total of 300 phenotypic and genetic correlations were estimated. For phenotypic and genetic correlations, 172 and 95 were significant, respectively. In general, most traits showing significant genetic correlations also showed significant phenotypic correlations. In this study, phenotypic and genetic correlations with NC milk suggest that many correlations between traits exist, making it difficult to predict the real consequences on the composition of milk, if selective breeding is applied on NC milk. We speculate that some of these consequences may lead to changes in the composition of milk, most likely affecting its physical and organoleptic properties. However, our results suggest that κ-casein could be used as an indicator trait to predict the occurrence of NC milk at the herd level.