The growing interest in plant-based food protein sources has provided opportunities for the valorization of agri-food by-products, driving the food industry towards more sustainable development. In this study, three extraction procedures (varying the pH value (7.0 and 11.0) and the addition of salt (0 and 5%)) were investigated to obtain seven different protein fractions (SIPF) from Sacha Inchi oil press-cake (SIPC), which were characterized in terms of their protein content, electrophoretic profile, secondary structure, and techno-functional properties. Extractions at pH 11.0 without salt addition produced the highest values of protein content, extraction yield, protein recovery, and protein concentration increase (84.0%, 24.7%, 36.5%, and 1.5-fold, respectively). Under these extraction conditions, the electrophoretic analysis indicated that most of the SIPC proteins were extracted. SIPF displayed an excellent oil absorption capacity (4.3–9.0w/w), and interesting foam activity (36.4–133.3%). The solubility and emulsifying activity of the albumin fractions were significantly higher than those of the other fractions (~87 vs. <15.8%, and 280–370 vs. <140 m2/g, respectively). Correlation analysis showed that the secondary structure of the SIPF significantly influences their techno-functional properties. These results indicate that SIPC is a by-product of great potential for protein extraction processes, and as a valorization strategy for technical cycle solutions for the Sacha Inchi productive chain in the circular economy context.