Moringa oleifera Lam. (Moringaceae) is a tropical plant native to India. It is widespread throughout the southern hemisphere, with great adaptability to high temperatures and water scarcity. Its seeds have a great amount of oil with a high content of oleic acid, quite similar to olive oil. Therefore, this study is focused on the extraction of oil from moringa seeds via an automatic screw press extractor at different temperatures (70, 100, 130, 160, 190, and 220 °C) and on the analysis of its acidity, acid value, peroxide value (PV), saponification value (SV), iodine value (IV), optical properties, and fatty acids profile. The results showed that the oil yield was 19 ± 3% regardless of the temperature applied. The oil was stable from the oxidative point of view, with a high acidity. Temperature extraction did not significantly affect the SV and the IV. However, the extraction temperature should be below 190 °C to obtain a translucent and luminous oil with light yellow tones. The oil contains high levels of unsaturated fatty acids, especially oleic acid (ω9) (up to 77.8%) and linolenic acid (ω3) (3.4%). On the other hand, behenic (7%), palmitic (6%), stearic (5%), and arachidic (0.2%) were the dominant saturated acids. The good properties of moringa oil make it a good, sustainable alternative to vegetable oils.