Composites made of linear low-density polyethylene (LLDPE) and β-cyclodextrin/<font style="font-variant: small-caps">d</font>-limonene inclusion complex (CD-lim) were prepared by melt extrusion to develop a novel food packaging material. Scanning electron microscopy evidenced a fairly good dispersion of the filler within the polymeric matrix. Infrared spectroscopy coupled with thermogravimetric analysis confirmed the presence of CD-lim in the composites, proving that the applied technology of including the essential oil within β-CD cages allows for preventing a sizable loss of <font style="font-variant: small-caps">d</font>-limonene despite a high temperature and shear applied upon extrusion processing. Moreover, the influence of the filler on the thermal properties of PE was assessed. It was found that the cyclodextrin-based inclusion complex significantly fastens the crystallization path of the polyethylene matrix with an improved crystallization rate of the PE/CD-lim composites compared to the neat polymer.