Virucidal properties of N-chlorosulfonamides immobilized on fibrous styrene-divinylbenzene copolymers have been studied. Corresponding materials with different functional group structures and chlorine content have been synthesized on FIBAN polymer carriers in the form of staple fibers and non-woven fabrics. The study has been conducted in general accordance with EN 14476 standard on poliovirus type-1 and adenovirus type-5. It has been found that all tested samples exhibit pronounced virucidal activity: regardless of the carrier polymer form, sodium N-chlorosulfonamides inactivated both viruses in less than 30 s, and N,N-dichlorosulfonamides—in 30–60 s. The main mechanism of action of these materials, obviously, consists in the emission of active chlorine from the functional group into the treated medium under the action of the amino groups of virus fragments and cell culture. Considering the previously described antimicrobial and reparative properties of such materials, as well as their satisfactory physical and mechanical properties, the synthesized polymers are promising for the creation of medical devices with increased resistance to microbial contamination, such as protective masks, filter elements, long-acting wound dressings, and others.