Biocompatible polymers are used for many different purposes (catheters, artificial heart components, dentistry products, etc.). An important field for biocompatible polymers is the production of vision implants known as intraocular lenses or custom-shape contact lenses. Typically, curved surfaces are manufactured by mechanical means such as milling, turning or lathe cutting. The 2.5 D objects/surfaces can also be manufactured by means of laser micromachining; however, due to the nature of light–matter interaction, it is difficult to produce a surface finish with surface roughness values lower than ~1 µm Ra. Therefore, laser micromachining alone can’t produce the final parts with optical-grade quality. Laser machined surfaces may be polished via mechanical methods; however, the process may take up to several days, which makes the production of implants economically challenging. The aim of this study is the investigation of the polishing capabilities of rough (~1 µm Ra) hydrophilic acrylic surfaces using bursts of femtosecond laser pulses. By changing different laser parameters, it was possible to find a regime where the surface roughness can be minimized to 18 nm Ra, while the polishing of the entire part takes a matter of seconds. The produced surface demonstrates a transparent appearance and the process shows great promise towards commercial fabrication of low surface roughness custom-shape optics.