Polypropylene (PP) fibrous membranes are widely used in medical and healthcare due to its sustainability. However, pristine PP fibrous membranes show poor flexibility, which limits their advanced functional application in medical and healthcare. Therefore, to improve the flexibility of PP fibrous membranes, propylene-based elastomer (PBE), a copolymer compatible with PP, was introduced by using the melt blowing technique in this study. The SEM images show that the PP/PBE fibrous membrane samples expressed a binary structured network morphology consisting of fibers with a diameter distribution ranging from 0.4 to 15 µm. With an increase in PBE mass ratio from 15 to 80 wt%, the frequency of fibers with a diameter <3 µm increased from 48.6 to 61.2%, thus making the elastic recovery rate in the machine direction (MD) increase from 62.9 to 80.3% and softness values increase from 15.88 to 54.31. Meanwhile, air permeability increased from 856 to 2257 m3/m2 · h as the mass per unit area of the samples decreased from 129.9 to 40.1 g/m2. This work provides an alternate method for producing flexible fibrous membranes that have potential for application in items such as surgical gown cuffs, bandages, and face mask ear loops.