Arthrospira platensis was used to obtain functional extracts through supercritical carbon dioxide extraction (SFE-CO₂). Pressure (P), temperature (T), co-solvent (CX), static extraction (SX), dispersant (Di) and dynamic extraction (DX) were evaluated as process parameters through a Plackett–Burman design. The maximum extract yield obtained was 7.48 ± 0.15% w/w. The maximum contents of bioactive metabolites in extracts were 0.69 ± 0.09 µg/g of riboflavin, 5.49 ± 0.10 µg/g of α-tocopherol, 524.46 ± 0.10 µg/g of β-carotene, 1.44 ± 0.10 µg/g of lutein and 32.11 ± 0.12 mg/g of fatty acids with 39.38% of palmitic acid, 20.63% of linoleic acid and 30.27% of γ-linolenic acid. A. platensis extracts had an antioxidant activity of 76.47 ± 0.71 µg GAE/g by Folin–Ciocalteu assay, 0.52 ± 0.02, 0.40 ± 0.01 and 1.47 ± 0.02 µmol TE/g by DPPH, FRAP and TEAC assays, respectively. These extracts showed antimicrobial activity against Staphylococcus aureus ATCC 25923, Pseudomonas aeruginosa ATCC 27853, Escherichia coli ATCC 25922 and Candida albicans ATCC 10231. Overall, co-solvent was the most significant factor for all measured effects (p < 0.05). Arthrospira platensis represents a sustainable source of bioactive compounds through SFE using the following extraction parameters P: 450 bar, CX: 11 g/min, SX: 15 min, DX: 25 min, T: 60 °C and Di: 35 g.