Fatty acid (FA) composition is a key component of sheep milk nutritional quality. However, breeding for FA composition in dairy sheep is hampered by the logistic and phenotyping costs. This study was aimed at estimating genetic parameters for sheep milk FA and to test the feasibility of their routine measurement by using Fourier-transform IR (FTIR) spectroscopy. Milk FA composition of 989 Sarda ewes farmed in 48 flocks was measured by gas chromatography (FAGC). Moreover, FTIR spectrum was collected for each sample, and it was used to predict FA composition (FAFTIR) by partial least squares regression: 700 ewes were used for estimating model parameters, whereas the remaining 289 animals were used to validate the model. One hundred replicates were performed by randomly assigning animals to estimation and validation data set, respectively. Variance components for both measured and predicted traits were estimated with an animal model that included the fixed effects of parity, days in milking interval, lambing month, province, altitude of flock location, the random effects of flock-test-date and animal genetic additive. Genetic correlations among FAGC, and between corresponding FAGC and FAFTIR were estimated by bivariate analysis. Coefficients of determination between FAGC and FAFTIR ranged from moderate (about 0.50 for odd- and branched-chain FA) to high (about 0.90 for de novo FA) values. Low-to-moderate heritabilities were observed for individual FA (ranging from 0.01 to 0.47). The largest value was observed for GC measured C16:0. Low–to-moderate heritabilities were estimated for FA groups. In most of cases, heritabilites were slightly larger for FAGC than FAFTIR. Estimates of genetic correlations among FAGC showed a large variability in magnitude and sign. The genetic correlation between FAFTIR and FAGC was higher than 60% for all investigated traits. Results of the present study confirm the existence of genetic variability of the FA composition in sheep and suggest the feasibility of using FAFTIR as proxies for these traits in large scale breeding programs.