In this work, we have studied the potential application for 3D-printing of a polymer made from combining a biodegradable and biocompatible polymer (i.e., polyhydroxybutyrate, PHB) with natural bio-based fiber (i.e., cellulose). To this end, a masterbatch at 15 wt.% in filler content was prepared by melt-blending, and then this system was “diluted” with pure PHB in a second extrusion phase in order to produce filaments at 1.5 and 3 wt.% of cellulose. For comparison, a filament made of 100% virgin PHB pellets was prepared under the same conditions. All the systems were then processed in the 3D-printer apparatus, and specimens were mainly characterized by static (tensile and flexural testing) and dynamic mechanical analysis. Thermogravimetric analysis, differential scanning calorimetry, spectroscopic measurements, and morphological aspects of PHB polymer and composites were also discussed. The results showed a significant negative impact of the process on the mechanical properties of the basic PHB with a reduction in both tensile and flexural mechanical properties. The PHB–cellulose composites showed a good dispersion filler in the matrix but a poor interfacial adhesion between the two phases. Furthermore, the cellulose had no effect on the melting behavior and the crystallinity of the polymer. The addition of cellulose improved the thermal stability of the polymer and minimized the negative impact of extrusion. The mechanical performance of the composites was found to be higher compared to the corresponding (processed) polymer.