This work explores for the first time the use of a fed-batch and continuous packed-bed millibioreactor for the chemoenzymatic oxidation of 2,5-furandicarboxaldehyde (DFF) to 2,5-furandicarboxylic acid (FDCA). Different operational variables were studied: temperature, substrate concentration, and flow rate using different reactors (batch, fed-batch, and a continuous packed-bed bioreactor). The best yield (100%) was achieved using the fed-batch reactor at an H2O2 flow rate of 3 µL/min with a substrate concentration (DFF) of 100 mM. Regarding the specific productivity, the highest values (>0.05 mg product/min g biocatalyst) were reached with the operation in the fed-batch bioreactor and the continuous packed-bed bioreactor. The yield of the biocatalyst decreased by 98% after the first reaction cycle during the operational stability tests, due to a substantial inactivation of the biocatalyst by H2O2 and peracid. In this study, it is possible to select the operational variables in fed-batch and continuous reactors for chemoenzymatic oxidation that can increase the yield and specific productivity; however, the stability of the biocatalyst should be improved in future research.