(1) Background: The COVID-19 pandemic lacks treatments; for this reason, the search for potential compounds against therapeutic targets is still necessary. Bioinformatics tools have allowed the rapid in silico screening of possible new metabolite candidates from natural resources or repurposing known ones. Thus, in this work, we aimed to select phytochemical candidates from Peruvian plants with antiviral potential against three therapeutical targets of SARS-CoV-2. (2) Methods: We applied in silico technics, such as virtual screening, molecular docking, molecular dynamics simulation, and MM/GBSA estimation. (3) Results: Rutin, a compound present in Peruvian native plants, showed affinity against three targets of SARS-CoV-2. The molecular dynamics simulation demonstrated the high stability of receptor–ligand systems during the time of the simulation. Our results showed that the Mpro-Rutin system exhibited higher binding free energy than PLpro-Rutin and NRutin systems through MM/GBSA analysis. (4) Conclusions: Our study provides insight on natural metabolites from Peruvian plants with therapeutical potential. We found Rutin as a potential candidate with multiple pharmacological properties against SARS-CoV-2.