Biobased and biodegradable polymers (BBDs) such as poly(3-hydroxy-butyrate), PHB, and poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) are considered attractive alternatives to fossil-based plastic materials since they are more environmentally friendly. One major problem with these compounds is their high crystallinity and brittleness. In order to generate softer materials without using fossil-based plasticizers, the suitability of natural rubber (NR) as an impact modifier was investigated in PHBV blends. Mixtures with varying proportions of NR and PHBV were generated, and samples were prepared by mechanical mixing (roll mixer and/or internal mixer) and cured by radical C–C crosslinking. The obtained specimens were investigated with respect to their chemical and physical characteristics, applying a variety of different methods such as size exclusion chromatography, Fourier-transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), thermal analysis, XRD, and mechanical testing. Our results clearly indicate that NR–PHBV blends exhibit excellent material characteristics including high elasticity and durability. Additionally, biodegradability was tested by applying heterologously produced and purified depolymerases. pH shift assays and morphology analyses of the surface of depolymerase-treated NR–PHBV through electron scanning microscopy confirmed the enzymatic degradation of PHBV. Altogether, we prove that NR is highly suitable to substitute fossil-based plasticizers; NR–PHBV blends are biodegradable and, hence, should be considered as interesting materials for a great number of applications.