A series of poly(ethylene glycol)--poly(sodium 4-styrenesulfonate) (PEG--PSSNa) copolymers were synthesized, and their antiviral activity against Zika virus (ZIKV) was determined. The polymers inhibit ZIKV replication in mammalian cells at nontoxic concentrations. The mechanistic analysis revealed that the PEG-PSSNa copolymers interact directly with viral particles in a zipper-like mechanism, hindering their interaction with the permissive cell. The antiviral activity of the copolymers is well-correlated with the length of the PSSNa block, indicating that the copolymers' ionic blocks are biologically active. The blocks of PEG present in copolymers studied do not hinder that interaction. Considering the practical application of PEG--PSSNa and the electrostatic nature of the inhibition, the interaction between the copolymers and human serum albumin (HSA) was evaluated. The formation of PEG--PSSNa-HSA complexes in the form of negatively charged nanoparticles well-dispersed in buffer solution was observed. That observation is promising, given the possible practical application of the copolymers.