Neurodegenerative diseases such as Alzheimer’s are very common today. Idebenone (IDE) is a potent antioxidant with good potential for restoring cerebral efficiency in cases of these and other medical conditions, but a serious drawback for the clinical use of IDE in neurological disorders lies in its scarce water solubility, which greatly inhibits its bioavailability. In this work, we prepared the inclusion complex of IDE with randomly methylated β-cyclodextrin (RAMEB), resulting in improved water solubility of the included drug; then its in vitro biological activity and ex vivo permeability was evalutated. The solid complex was characterized through FT-IR spectroscopy, Thermogravimetric analysis (TGA) and Differential Scanning Calorimetry (DSC). A 78-fold improvement of the solubility of IDE in water resulted, together with a strong 1:1 host–guest interaction (association constant of 12630 M−1), and dissolution of the complex within 15 min, all evidenced during the in-solution studies. Biological in vitro studies were then performed on differentiated human neuroblastoma cells (SH-SY5Y) subjected to oxidative stress. Pretreatment with IDE/RAMEB positively affected cell viability, promoted the nuclear translocation of Nrf2, and increased the levels of GSH as well as those of the endogenous antioxidant enzymes Mn-SOD and HO-1. Lastly, the complexation significantly improved the permeation of IDE through isolated rat nasal mucosa.