There is a growing demand for polymer fiber scaffolds for biomedical applications and tissue engineering. Biodegradable polymers such as polycaprolactone have attracted particular attention due to their applicability to tissue engineering and optical neural interfacing. Here we report on a scalable and inexpensive fiber fabrication technique, which enables the drawing of PCL fibers in a single process without the use of auxiliary cladding. We demonstrate the possibility of drawing PCL fibers of different geometries and cross‐sections, including solid‐core, hollow‐core, and grooved fibers. The solid‐core fibers of different geometries are shown to support cell growth, through successful MCF‐7 breast cancer cell attachment and proliferation. We also show that the hollow‐core fibers exhibit a relatively stable optical propagation loss after submersion into a biological fluid for up to 21 days with potential to be used as waveguides in optical neural interfacing. The capacity to tailor the surface morphology of biodegradable PCL fibers and their non‐cytotoxicity make the proposed approach an attractive platform for biomedical applications and tissue engineering.