Cyanobacteria are a rich source of bioactive compounds, mainly in the Arthospira sp., and one of the most interesting components in recent years has been C-phycocyanin (C-PC). There have been several conventional methods for their extraction, among which stand out: chemical products, freezing-thawing (FT); enzymatic, and maceration (M); which have come to be replaced by more environmentally friendly methods, such as those assisted by microwaves (MW) and high-pressure homogenization (HPH). The aim of the research was to use these two “green extraction processes” to obtain C-PC from cyanobacteria Arthrospira maxima because they improve functionality and are fast. Extractions of C-PC were studied by means of two experimental designs for MW and HPH, based on a response surface methodology (RSM) employing, firstly, a factorial design 33: power (100, 200, and 300 W), time (15, 30, and 60 s), and types of solvents (distiller water, Na-phosphate buffer and, distiller water: Na-phosphate buffer (Ph 7.0; 1:1, v/v); and secondly, two factors with different levels: Pressure (800, 1000, 1200, 1400, and 1600 bar) and, types of solvents (distilled water, Na-phosphate buffer (pH 7.0) 100 mM and, Na-phosphate buffer:water 1:1, (v/v)). Optimum C-PC content was achieved with the HPH process under Na-phosphate solvent at 1400 bar (291.9 ± 6.7 mg/g) and the MW method showed improved results using distilled water as a solvent at 100 W for 30 s (215.0 ± 5.5 mg/g). In the case of conventional methods, the freeze–thawing procedure reached better results than maceration using the buffer (225.6 ± 2.6 mg/g). This last one also did not show a significant difference between solvents (a range of 147.7–162.0 mg/g). Finally, the main advantage of using green extractions are the high C-PC yield achieved, effectively reducing both processing times, costs, and increasing the economic and functional applications of the bioactive compound.