Whey from goat and sheep have been gaining attention in the last few years for their nutritional properties. Unfortunately, β-Lg, not found in human milk, may trigger infant allergies if used in infant food formulations, so there is a growing interest in developing ingredients derived from whey with higher α-La/β-Lg ratios. The objective of this work was to study the effect of high-pressure processing (HPP) on caprine and ovine native whey concentrates (NWC) in order to obtain α-Lactalbumin (α-La)-enriched fractions. NWCs were treated at 600 MPa (23 °C) for 2, 4, and 15 min and two pH conditions were studied (physiological pH and pH 4.60). The concentration of β-Lg in supernatant fraction after HPP significantly decreased after 2 min of treatment, while the concentration of α-La was unchanged in both goat and sheep samples. Longer HPP processing times (up to 15 min) progressively increased α-La purification degree but also decreased the α-La yield. Caprine and ovine NWCs treated at physiological pH provided better α-La yield, α-La purification degree, and higher β-Lg precipitation degrees than the corresponding acidified samples, while the corresponding NWC supernatant (NWCsup) showed lower values for both surface hydrophobicity and total free thiol indices, suggesting a higher extent of protein aggregation. Effects of sample acidification and the HPP treatment were opposite to those previously reported on bovine NWC, so further characterization of caprine and ovine β-Lg should be carried out to understand their different behavior.