Plants and their derived molecules have been traditionally used to manage numerous pathological complications, including male erectile dysfunction (ED). Mimosa pudica Linn. commonly referred to as the touch-me-not plant, and its extract are important sources of new lead molecules in drug discovery research. The main goal of this study was to predict highly effective molecules from M. pudica Linn. for reaching and maintaining penile erection before and during sexual intercourse through in silico molecular docking and dynamics simulation tools. A total of 28 bioactive molecules were identified from this target plant through public repositories, and their chemical structures were drawn using Chemsketch software. Graph theoretical network principles were applied to identify the ideal target (phosphodiesterase type 5) and rebuild the network to visualize the responsible signaling genes, proteins, and enzymes. The 28 identified bioactive molecules were docked against the phosphodiesterase type 5 (PDE5) enzyme and compared with the standard PDE5 inhibitor (sildenafil). Pharmacokinetics (ADME), toxicity, and several physicochemical properties of bioactive molecules were assessed to confirm their drug-likeness property. Molecular dynamics (MD) simulation modeling was performed to investigate the stability of PDE5–ligand complexes. Four bioactive molecules (Bufadienolide (−12.30 kcal mol−1), Stigmasterol (−11.40 kcal mol−1), Isovitexin (−11.20 kcal mol−1), and Apigetrin (−11.20 kcal mol−1)) showed the top binding affinities with the PDE5 enzyme, much more powerful than the standard PDE5 inhibitor (−9.80 kcal mol−1). The four top binding bioactive molecules were further validated for a stable binding affinity with the PDE5 enzyme and conformation during the MD simulation period as compared to the apoprotein and standard PDE5 inhibitor complexes. Further, the four top binding bioactive molecules demonstrated significant drug-likeness characteristics with lower toxicity profiles. According to the findings, the four top binding molecules may be used as potent and safe PDE5 inhibitors and could potentially be used in the treatment of ED.