Adeno-associated viruses (AAVs) are one of the most promising tools for gene therapy applications. These vectors are purified using affinity and ion exchange chromatography, typically using packed beds of resin adsorbents. This leads to diffusion and pressure drop limitations that affect process productivity. Due to their high surface area and porosity, electrospun nanofiber adsorbents offer mass transfer and flow rate advantages over conventional chromatographic media. The present work investigated the use of affinity cellulose-based nanofiber adsorbents for adeno-associated virus serotype 5 (AAV5) capture, evaluating dynamic binding capacity, pressure drop, and AAV5 recovery at residence times (RT) less than 5 s. The dynamic binding capacity was found to be residence time-dependent, but nevertheless higher than 1.0 × 1014TP mL−1(RT = 1.6 s), with a pressure drop variation of 0.14 MPa obtained after loading more than 2,000 column volumes of clarified AAV5 feedstock. The single affinity chromatography purification step using these new affinity adsorbents resulted in 80% virus recovery, with the removal of impurities comparable to that of bead-based affinity adsorbents. The high binding capacity, virus recovery and reduced pressure drop observed at residence times in the sub-minute range can potentially eliminate the need for prior concentration steps, thereby reducing the overall number of unit operations, process time and costs.