Antioxidant nanobiocomposites based on poly(ε-caprolactone) (PCL) were prepared by incorporating hydroxytyrosol (HT) and a commercial montmorillonite, Cloisite30B (C30B), at different concentrations. A full structural, thermal, mechanical, and functional characterization of the developed nanobiocomposites was carried out. The presence of the nanoclay and HT increased PCL crystallinity, whereas some decrease in thermal stability was observed. TEM analyses corroborated the good dispersion of C30B into the PCL macromolecular structure as already asserted by XRD tests, because no large aggregates were observed. A reduction in oxygen permeability and an increase in elastic modulus were obtained for films containing the nanoclay. Finally, the presence of the nanoclay produced a decrease in the HT release from films due to some interaction between HT and C30B. Results proved that these nanobiocomposites can be an interesting and environmentally friendly alternative for active food packaging applications with antioxidant performance.