The spike protein (SP) of SARS-CoV-2 (SC-2) is susceptible to high mutation and has contributed to the multiple waves of COVID-19 being experienced. Hence, targeting the SP remains a logical approach in the development of potent therapeutics against SARS-CoV-2. Here, a computational technique was adopted to identify broad-spectrum plant secondary metabolites with indigenous relevance in the management of respiratory infections against the SPs of the SC-2 wild- type (SC-2WT) and omicron variants. Following 100 ns molecular dynamic (MD) simulation and binding free energy calculation of the top five compounds identified through molecular docking, maysin (SC-2WT (−34.85 kcal/mol), omicron (−38.88 kcal/mol)) and geraniin (SC-2WT (−36.90 kcal/mol) omicron (−31.28 kcal/mol)) had better broad-spectrum activities for the investigated SPs than zafirlukast (SC-2WT (−33.73 kcal/mol) omicron (−22.38 kcal/mol)). Furthermore, 6-hydroxycyanidin-3-rutinoside (−42.97 kcal/mol) and kaempferol-7-glucoside (−37.11 kcal/mol) had the best affinity for the SPs of omicron and SC-2WT, respectively. Interestingly, except for Kaempferol-7-glucoside against omicron SP, all the top-ranked compounds were thermodynamically stable with the SP of both variants, and this observation was linked to the number, nature, and bond length in the resulting complexes in each case. Also, except for geraniin, all the top-ranked compounds had lower toxicity profiles compared to zafirlukast and this could be attributed to their phenolic moieties. Nevertheless, the in vitro and in vivo confirmation of the activities observed in this study is recommended, especially for maysin and geraniin with the best broad-spectrum activity, towards development of COVID-19 drug candidates.