Background and aim: Novel nature of the viral pathogen SARS-CoV-2 and the absence of standard drugs for treatment, have been a major challenge to combat this deadly infection. Natural products offer safe and effective remedy, for which traditional ethnic medicine can provide leads. An indigenous poly-herbal formulation, Kabasura Kudineer from Siddha system of medicine was evaluated here using a combination of computational approaches, to identify potential inhibitors against two anti-SARS-CoV-2 targets - post-fusion Spike protein (structural protein) and main protease (Mpro, non-structural protein). Experimental procedure: We docked 32 phytochemicals from the poly-herbal formulation against viral post-fusion Spike glycoprotein and Mpro followed by molecular dynamics using Schrodinger software. Drug-likeness analysis was performed using machine learning (ML) approach and pkCSM. Results: The binding affinity of the phytochemicals in Kabasura Kudineer revealed the following top-five bioactives: Quercetin > Luteolin > Chrysoeriol > 5-Hydroxy-7,8-Dimethoxyflavone > Scutellarein against Mpro target, and Gallic acid > Piperlonguminine > Chrysoeriol > Elemol > Piperine against post-fusion Spike protein target. Quercetin and Gallic acid exhibited binding stability in complexation with their respective viral-targets and favourable free energy change as revealed by the molecular dynamics simulations and MM-PBSA analysis. Conclusion: These outcomes provide: (a) potential mechanism for the anti-viral efficacy of the indigenous Siddha formulation, targeting Mpro and post-fusion Spike protein (b) top bioactive lead-molecules that may be developed as natural product-based anti-viral pharmacotherapy and their pleiotropic protective effects may be leveraged to manage co-morbidities associated with COVID-19.