Conventional cyclodextrin complexation enhances the solubility of poorly soluble drugs but is solvent-intensive and environmentally unfavorable. This study evaluated solvent-free hot-melt extrusion (HME) for forming cyclodextrin inclusion complexes to improve the solubility and dissolution of ibuprofen (IBU). Molecular docking confirmed IBU’s hosting in Hydroxypropyl-β-cyclodextrin (HPβ-CD), while phase solubility revealed its complex stoichiometry and stability. In addition, an 11 mm twin-screw co-rotating extruder with PVP VA-64 as an auxiliary substance aided the complex formation and extrusion. Using QbD and the Box–Behnken design, we studied variables (barrel temperature, screw speed, and polymer concentration) and their impact on solubility and dissolution. The high polymer concentration and high screw speeds positively affected the dependent variables. However, higher temperatures had a negative effect. The lowest barrel temperature set near the Tg of the polymer, when combined with high polymer concentrations, resulted in high torques in HME and halted the extrusion process. Therefore, the temperature and polymer concentration should be selected to provide sufficient melt viscosities to aid the complex formation and extrusion process. Studies such as DSC and XRD revealed the amorphous conversion of IBU, while the inclusion complex formation was demonstrated by ATR and NMR studies. The dissolution of ternary inclusion complexes (TIC) produced from HME was found to be ≥85% released within 30 min. This finding implied the high solubility of IBU, according to the US FDA 2018 guidance for highly soluble compounds containing immediate-release solid oral dosage forms. Overall, the studies revealed the effect of various process parameters on the formation of CD inclusion complexes via HME.