Yellow maize kernels were subjected to supercritical carbon dioxide (SC-CO) extraction to obtain a lutein-rich extract with potential nutraceutical properties. SC-CO extraction parameters (pressure and temperature) were optimized by employing a full-factorial (3) design of experiments and response surface methodology, based on yield of lutein, antioxidant activity, and ω-6/ω-3 fatty acid ratio of the extracts. A Chrastil equation was also developed for predicting the solubility of lutein in SC-CO under different extraction conditions. The optimized extraction condition was obtained at 500 bar, 70 °C for 90 min, at which the extract was found to possess a unique combination of the highest lutein yield (275.00 ± 3.50 μg/g of dry weight), along with a well-balanced ω-6/ω-3 fatty acid ratio (3:1). Moreover, the total phenol content and antioxidant activity were also found to be the highest at this condition. This lutein-rich extract is a promising nutraceutical or dietary supplement in the food industry.