We investigated the melt-spinning potential of a poly(3-hydroxybutyrate)/poly(3-hydroxybutyrate-co-4-hydroxybutyrate) blend using a piston spinning machine with two different spinneret diameters (0.2 and 0.5 mm). Results from the differential scanning calorimetry, dynamic mechanical thermal analysis, and tensile testing showed distinct filament properties depending on the monofilaments’ cross-sectional area. Finer filaments possessed different melting behaviors compared to the coarser filaments and the neat polymer, indicating the formation of a different type of polymer crystal. Additionally, the mechanical properties of the finer filament (tensile strength: 21.5 MPa and elongation at break: 341%) differed markedly from the coarser filament (tensile strength: 11.7 MPa, elongation at break: 12.3%). The hydrolytic stability of the filaments was evaluated for 7 weeks in a phosphate-buffered saline solution and showed a considerably reduced elongation at break of the thinner filaments. Overall, the results indicate considerable potential for further filament improvements to facilitate textile processing.