The broad utilization of electrospun scaffolds of sodium alginate in tissue engineering is strongly limited by their high solubility in aqueous environments and by the difficulty to adjust their degradation dynamics. Here, an alternative strategy to enhance the stability and to control the degradability of alginate nanofibers is described by treating them with trifluoroacetic acid for specific time intervals. It is demonstrated that, by increasing the duration of the acid treatment procedure, a lower degradation rate of the resulting fibers in buffer solutions can be achieved. Furthermore, the produced mats are free from cytotoxic compounds and are highly biocompatible. The properties conferred to the alginate nanofibrous mats by the proposed method are extremely attractive in the production of innovative biomedical devices.