Structured surfaces exhibit functional properties that can enhance the performance of a bioimplant in terms of biocompatibility, adhesion, or corrosion behavior. In order to tailor the surface property, chemical and physical methods can be used in a sequence of many steps. On the other hand, laser surface processing can provide a single step solution to achieve the designated surface function with the use of simpler equipment and high repeatability. This work provides the details on the surface structuring of AZ31, a biocompatible and biodegradable Mg alloy, by a single-step laser surface structuring based on remelting. The surfaces are characterized in terms of topography, chemistry, and physical integrity, as well as the effective change in the surface wetting behavior is demonstrated. The results imply a great potential in local or complete surface structuring of medical implants for functionalization by the flexible positioning of the laser beam.