Investigations into cholinesterase inhibition have received attention from researchers in recent years for the treatment of Alzheimer’s disease. Cholinesterase enzymes, namely, acetylcholinesterase (AChE) and butyrylcholinesterase (BChE), hold pivotal significance in Alzheimer’s disease (AD) treatment. In this study, we utilized the ethanolic extract of Astragalus crenatus followed by liquid chromatography–electrospray ionization tandem mass spectrometry (LC-ESI-MS/MS) to separate and identify at least 21 compounds in the extract. Rosmarinic acid exhibited the highest concentration (96.675 ± 1.3 mg/g extract), succeeded by hesperidin (79.613 ± 1.2 mg/g extract), hesperetin (75.102 ± 1.4 mg/g extract), rutin (68.156 ± 1.6 mg/g extract), chlorogenic acid (67.645 ± 1.5 mg/g extract), fisetin (66.647 ± 2.3 mg/g extract), and hyperoside (63.173 ± 1.5 mg/g extract). A. crenatus extract efficiently inhibited both AChE and BChE activities in a dosage-dependent manner. Molecular docking was employed to scrutinize the anticholinesterase mechanisms of the identified phytocompounds. Notably, a network pharmacology analysis was executed for the most efficacious compound. Based on binding energies, hesperidin emerged as the most potent inhibitor against both AChE and BChE, exhibiting scores of −10.5 Kcal/mol and −9.8 Kcal/mol, respectively. Due to its dual inhibition of AChE and BChE activities, hesperidin from Astragalus crenatus holds promise for the development of novel therapeutics aimed at neurological disorders, particularly AD.