Gestation and the neonatal period are crucial periods in infant development. Many components of breast milk, including fatty acids, play an important role in strengthening the immune system. The aim of our research was to evaluate the fatty acid profiles of milk from 69 mothers, including subjects having a normal weight, obesity, or gestational diabetes. For the analyses, we used gas chromatography (GC) with flame ionization detection (FID) and GC coupled with mass spectrometry (GC/MS). The main fatty acids found in breast milk were palmitic acid (C16:0; 26–28%), linoleic acid (C18:2; 23–28%), and α-linolenic acid linoleic acid (C18:3; 15–17%), followed by myristic acid (C14:0; 5–8%), lauric acid (C12:0; 4–6%) and stearic acid (C18:0; 4–5%). The average breakdown of fatty acids was 50% saturated, 44% polyunsaturated, and 6% monounsaturated. Breast milk samples were classified using principal component analysis and linear discriminant analysis. Results showed that milk from the two major groups of obese and normal body mass index (BMI) could be distinguished with an accuracy of 89.66%. Breast milk samples of Hungarian and Ukrainian mothers showed significant differences based on the fatty acid composition, which variations are attributable to the mothers’ dietary habits.