Here, we evaluated the effect of dietary supplementation with an Olea europaea L. extract on the animal welfare and milk quality of dairy cows. Thirty Italian Holstein–Friesian dairy cows in the mid-lactation phase (90 to 210 days) were blocked into experimental groups based on parity class (namely, primiparous (P) (n = 10), secondiparous (S) (n = 10) and pluriparous (PL) (n = 10)) and received, for 60 days, Phenofeed Dry® at 500 mg/cow/day. Milk and blood samples were collected before the start of the treatment (T0), subsequently every 15 days (T1–T4) and at 45 days after the end of treatment (T5). In the serum, glucose and triglycerides, stress, the thyroid, lactation and sex hormones were measured; in the milk, lysozyme content as well as the fatty acid profile were assessed. In the whole animal, the enriched feed helped to maintain hormonal parameters in the physiological range while producing hypoglycemic (T4 vs. T0, for P and PL p < 0.001) and hypolipidemic effects (T4 vs. T0, for P p < 0.001 and for PL p < 0.01). At the milk level, it resulted in a reduction in total fat (T5 vs. T0, for P, S and PL p < 0.001) and in the saturated fatty acids (SFAs)/monounsaturated fatty acids (MUFAs) ratio paralleled by an increase in polyunsaturated fatty acids (PUFAs) (T5 vs. T0, for P, S and PL p < 0.001), protein content (lysozyme (T4 vs. T0, for P and PL p < 0.001)) and lactose (T5 vs. T0, for P, S and PL p < 0.001). Thus, the inclusion of natural bioactive molecules such as O. europaea L. polyphenols in the dairy cow diet may help to improve animal welfare and milk quality.