Association analyses between candidate genes and bovine milk fatty acids can improve our understanding of genetic variation in milk fatty acid profiles and reveal potential opportunities to tailor milk fat composition through selection strategies. In this work, we investigated the association of 51 single nucleotide polymorphisms (SNP) selected from 37 candidate genes using a functional and positional approach, with 47 fatty acids, 9 fatty acid groups, and 5 Δ(9)-desaturation indices in milk samples from Brown Swiss cows. Individual milk samples were collected from 1,158 Italian Brown Swiss cows, and gas chromatography was used to obtain detailed milk fatty acid compositions. A GoldenGate assay system (Illumina, San Diego, CA) was used to perform genotype 96 selected SNP located in 54 genes across 22 chromosomes. In total, 51 polymorphic SNP in 37 candidate genes were retained for the association analysis. A Bayesian linear animal model was used to estimate the contribution of each SNP. A total of 129 tests indicated relevant additive effects between a given SNP and a single fatty acid trait; 38 SNP belonging to 30 genes were relevant for a total of 57 fatty acid traits. Most of the studied fatty acid traits (~81%) were relevantly associated with multiple SNP. Relevantly associated SNP were mainly found in genes related to fat metabolism, linked to or contained in previously identified quantitative trait loci for fat yield or content, or associated with genes previously identified in association analyses with milk fatty acid profiles in other cow breeds. The most representative candidate genes were LEP, PRL, STAT5A, CCL3, ACACA, GHR, ADRB2, LPIN1, STAT1, FABP4, and CSN2. In particular, relevant associations with SNP located on bovine chromosome 19 (BTA19) were found. Two candidate genes on BTA19 (CCL3 and ACACA) were relevantly associated with de novo short- and medium-chain fatty acids, likely explaining the high heritability values found for these fatty acids (with the exception of C6:0). Two additional genes on BTA19 (CCL2 and GH1) showed associations with saturated and branched-chain fatty acids. Our findings provide basic information on genes and SNP affecting the milk fatty acid composition of dairy cows. These results may support the possibility of using genetic selection to modify milk fatty acid profiles to promote beneficial health-related effects.