The aim of this study was to enhance the apparent solubility and dissolution properties of flurbiprofen through inclusion complexation with cyclodextrins. Especially, the efficacy of supercritical fluid technology as a preparative technique for the preparation of flurbiprofen–methyl-β-cyclodextrin inclusion complexes was evaluated. The complexes were prepared by supercritical carbon dioxide processing and were evaluated by solubility, differential scanning calorimetry, X-ray powder diffraction, scanning electron microscopy, practical yield, drug content estimation and in vitro dissolution studies. Computational molecular docking studies were conducted to study the possibility of molecular arrangement of inclusion complexes between flurbiprofen and methyl-β-cyclodextrin. The studies support the formation of stable molecular inclusion complexes between the drug and cyclodextrin in a 1:1 stoichiometry. In vitro dissolution studies showed that the dissolution properties of flurbiprofen were significantly enhanced by the binary mixtures prepared by supercritical carbon dioxide processing. The amount of flurbiprofen dissolved into solution alone was very low with 1.11 ± 0.09% dissolving at the end of 60 min, while the binary mixtures processed by supercritical carbon dioxide at 45 °C and 200 bar released 99.39 ± 2.34% of the drug at the end of 30 min. All the binary mixtures processed by supercritical carbon dioxide at 45 °C exhibited a drug release of more than 80% within the first 10 min irrespective of the pressure employed. The study demonstrated the single step, organic solvent-free supercritical carbon dioxide process as a promising approach for the preparation of inclusion complexes between flurbiprofen and methyl-β-cyclodextrin in solid-state.