Additive manufactured parts often require post-processing to obtain the desired surface finish. In this sense, this work investigates the ball burnishing process's applicability as a finishing method for fused filament fabricated (FFF) parts. Ball burnishing is a mechanical finishing procedure based on the plastic deformation of the treated surface that could provide significant advantages, as it is non-abrasive and does not chemically interact with the model material. Following Taguchi's design methodology, optimal values of four burnishing parameters have been identified, and significant improvements in surface quality have been quantitatively and qualitatively proven. Mechanical performance under tensile and flexural loading, impact testing, and bending fatigue of ball-burnished samples has been compared to pristine values. Besides the enhanced surface quality of the samples, a notable finding of the study is a minimum twofold increase in the fatigue life of ball-burnished samples, as well as a higher impact energy absorption. Accordingly, this research provides experimental evidence to set ball burnishing as a novel post-processing technique for FFF parts.