Seasonal human influenza is a serious respiratory infection caused by influenza viruses that can be found all over the world. Type A influenza is a contagious viral infection that, if left untreated, can lead to life-threatening consequences. Fortunately, the plant kingdom has many potent medicines with broad-spectrum antiviral activity. Herein, six plant constituents, namely Tanshinone IIA 1, Carnosic acid 2, Rosmarinic acid 3, Glycyrrhetinic acid 4, Baicalein 5, and Salvianolic acid B 6, were screened for their antiviral activities against H1N1 virus using in vitro and in silico approaches. Hence, their anti-influenza activities were tested in vitro to determine inhibitory concentration 50 (IC) values after measuring their CC values using MTT assay on MDCK cells. Interestingly, Tanshinone IIA (TAN) 1 was the most promising member with CC = 9.678 μg/ml. Moreover, the plaque reduction assay carried on TAN 1 revealed promising viral inhibition percentages of 97.9%, 95.8%, 94.4%, and 91.7% using concentrations 0.05 μg/μl, 0.025 μg/μl, 0.0125 μg/μl, and 0.006 μg/μl, respectively. Furthermore, in silico molecular docking disclosed the superior affinities of Salvianolic acid B (SAL) 6 towards both surface glycoproteins of influenza A virus (namely, hemagglutinin (HA) and neuraminidase (NA)). The docked complexes of both SAL and TAN inside HA and NA receptor pockets were selected for 100 ns MD simulations followed by MM-GBSA binding free energy calculation to confirm the docking results and give more insights regarding the stability of both compounds inside influenza mentioned receptors, respectively. The selection criteria of the previously mentioned complexes were based on the fact that SAL showed the highest docking scores on both viral HA and NA glycoproteins whereas TAN achieved the best inhibitory activity on the other hand. Finally, we urge more advanced preclinical and clinical research, particularly for TAN, which could be used to treat the human influenza A virus effectively.