Cell motion and in particular amoeboid migration is crucial for the survival of living organisms. To advance biomedical research, a constant need for novel materials and surface structures arises, improving immigration of cells into artificial structures used for tissue engineering and for advancing therapy in modern medicine. This work focuses on investigating amoeboid single-cell migration on intrinsically nano-structured, biodegradable silica fibers in comparison to chemically equivalent plain glass surfaces. Cell migration trajectories are classified into directed runs and quasi-random migration by a local mean squared displacement (LMSD) analysis. We find that directed movement on silica fibers is enhanced in a significant manner by the fibers' nanoscale surface-patterns. Further, cell adhesion on the silica fibers is a microtubule-mediated process. Cells lacking microtubules detach from the fibers, but adhere well to glass surfaces. Knock-out mutants of myosin II migrating on the fibers are as active as cells with active myosin II, while the migration of the knock-out mutants is hindered on plain glass. Identifying relevant cytoskeletal compounds for cell migration in 2D vs. 3D will help to optimize materials or surfaces that boost specific migration strategies to open up new opportunities for innovative diagnostic and therapeutic concepts