Currently, Bixa orellana L. extracts are used as a color source in the food, pharmaceutical, and cosmetic industries because they are important as a potential source of antioxidant activity. The extraction is carried out by conventional methods, using alkaline solutions or organic solvents. These extraction methods do not take advantage of the lipid fraction of annatto (Bixa orellana L.) seeds, and the process is not friendly to the environment. In this work, the objective was to obtain an extract rich in nutraceuticals (bixin and tocols) of high antioxidant power from Peruvian annatto seeds as a potential source for a functional food or additive in the industry using supercritical fluid extraction (SFE). Experiments related to extraction yield, bixin, tocotrienols, tocopherols, and antioxidant activity were carried out. The SFE was performed at 40 °C, 50 °C, and 60 °C, and 100, 150, and 250 bar with 0.256 kg/h carbon dioxide as the supercritical solvent (solvent-to-feed ratio of 10.2). Supercritical extraction at 60 °C and 250 bar presented the best results in terms of global extraction yield of 1.40 ± 0.01 g/100 g d.b., extract concentration of 0.564 ± 0.005 g bixin/g extract, 307.8 mg α-tocotrienol/g extract, 39.2 mg β-tocotrienol/g extract, 2 mg γ-tocopherol/g extract, and IC50 of 989.96 μg extract/mL. Economical evaluation showed that 60 °C, 250 bar, and 45 min presented the lowest cost of manufacturing (2 × 2000 L, COM of USD 212.39/kg extract). This extract is a potential source for functional food production.