Zika virus (ZIKV) continues to pose a significant global health threat due to its association with severe neurological complications, including congenital microcephaly and Guillain–Barré syndrome. Despite its public health impact, no specific antiviral drugs or vaccines are currently available, highlighting the urgent need for novel therapeutic candidates. Medicinal plants such as Euphorbia hirta and Bacopa monnieri are rich in bioactive phytochemicals known for their antiviral, anti-inflammatory, and neuroprotective activities. The present study undertakes an integrated in silico investigation to evaluate the anti-Zika potential of phytochemicals derived from these two plants using molecular docking, ADMET analysis, and Density Functional Theory (DFT) calculations. Molecular docking was performed against key ZIKV target proteins—NS1, NS3 protease, and Envelope protein EDIII—to assess binding affinity and inhibitory potential. ADMET profiling was conducted to examine pharmacokinetic suitability, while DFT descriptors, including HOMO–LUMO energies and dipole moment, were evaluated to determine molecular reactivity and stability. Among the screened phytochemicals, galloylquinic acid, Bacopaside III, and Bacopaside A exhibited the strongest binding affinities and acceptable ADMET profiles, along with favorable quantum chemical characteristics. The findings suggest that these phytocompounds have promising multi-target inhibitory activity and merit further in vitro and in vivo validation as natural anti-Zika therapeutic candidates.