The optimization of the supercritical fluid extraction (SFE) of cannabinoids, using supercritical carbon dioxide (scCO2), was investigated in a fractional factorial design study. It is hypothesized that four main parameters (temperature, pressure, dry flower weight, and extraction time) play an important role. Therefore, these parameters were screened at predetermined low, medium, and high relative levels. The density of scCO2 was used as a factor for the extraction of cannabinoids by changing the pressure and temperature. The robustness of the mathematical model was also evaluated by regression analysis. The quantification of major (cannabidiol (CBD), cannabidiolic acid (CBDA), delta 9-tetrahydrocannabinol (Δ9-THC), delta 8-tetrahydrocannabinol (Δ8-THC), and delta 9-tetrahydrocannabinol acid (THCA-A)) and minor (cannabidivann (CBDV), tetrahydrocannabivann (THCV), cannabigerolic acid (CBG), cannabigerol (CBGA), cannabinol (CBN), and cannabichomere (CBC)) cannabinoids in the scCO2 extract was performed by RP-HPLC analysis. From the model response, it was identified that long extraction time is a significant parameter to obtain a high yield of cannabinoids in the scCO2 extract. Higher relative concentrations of CBD(A) (0.78 and 2.41% w/w, respectively) and THC(A) (0.084 and 0.048% w/w, respectively) were found when extraction was performed at high relative pressures and temperatures (250 bar and 45 °C). The higher yield of CBD(A) compared to THC(A) can be attributed to the extract being a CBD-dominant cannabis strain. The study revealed that conventional organic solvent extraction, e.g., ethanol gives a marginally higher yield of cannabinoids from the extract compared to scCO2 extraction. However, scCO2 extraction generates a cleaner (chlorophyll-free) and organic solvent-free extract, which requires less downstream processing, such as purification from waxes and chlorophyll.