Novel electrochemical DNA-based biosensors with outer-sphere Nafion and chitosan protective membranes were prepared for the evaluation of antioxidant properties of beverages (beer, coffee, and black tea) against prooxidant hydroxyl radicals. A carbon working electrode of a screen-printed three-electrode assembly was modified using a layer-by-layer deposition technique with low molecular weight double-stranded DNA and a Nafion or chitosan film. The membrane-covered DNA biosensors were initially tested with respect to their voltammetric and impedimetric response after the incubation of the beverage and the medium exchange for the solution of the redox indicator [Fe(CN)6]3−/4−. While the Nafion-protected biosensor proved to be suitable for beer and black tea extracts, the chitosan-protected biosensor was successfully used in a coffee extract. Afterwards, the applicability was successfully verified for these biosensors for the detection of a deep degradation of the surface-attached DNA at the incubation in the cleavage agent (hydroxyl radicals generated via Fenton reaction) and for the evaluation of antioxidant properties of coffee and black tea extracts against prooxidant hydroxyl radicals. The investigation of the novel biosensors with a protective membrane represents a significant contribution to the field of electrochemical DNA biosensors utilization.