The effects of alpha- and gamma-cyclodextrins (α- and γ-CDs) on the thermal and crystal nucleation behavior of electrospun poly(ε-caprolactone) (PCL) nanofibers have been investigated. PCL/CD composite nanofibers were obtained for the first time by electrospinning the mixture from chloroform/N,N-dimethylformamide (60:40). Scanning electron microscopy analyses indicated that neat PCL nanofibers have an average diameter of 400 nm, which increases with the addition of CDs. The presence of CDs on or in the electrospun PCL fibers in the electrospun mats was investigated using Fourier transform infrared spectroscopy, thermogravimetric analysis, and wide-angle X-ray diffraction analysis. Differential scanning calorimetry showed that the PCL/CD composite fibers exhibit higher crystallization temperatures and sharper crystallization exotherms with increased CD loading, indicating the ability of CDs to nucleate PCL crystallization. Water contact angle (WCA) measurements indicate an inverse relationship between WCA and α- or γ-CD concentration up to 30% loading. Phenolphthalein absorption tests were performed to study the kinetics of their inclusion complex (IC) formation with CDs. Unexpectedly, γ-CD-functionalized nanowebs performed better than α-CD. This might be because at elevated loadings some α-CDs may have threaded over PCL chains and formed ICs, whereas γ-CD did not. With their encapsulation capabilities and their lowered hydrophobicity, PCL/CD composite fibers might have potential uses in medical applications, in particular as wound odor absorbants in dressings, because it is well known that CDs can form ICs with these odorants, thereby effectively removing them.