Lysine-specific demethylase 1 (LSD1) has recently emerged as a therapeutic target for cancer. However, almost all LSD1 inhibitors developed to date are chemo-synthesised molecules. In this study, the LSD1 inhibitory activity of 12 natural flavones, including four aglycones and their corresponding monoglycosides and diglucosides, was evaluated. Based on the structure–activity relationships, LSD1 inhibition activity was greater for flavonoid monoglycosides than their aglycones lacking the sugar moiety. The effects of isoquercitrin, which exhibited optimal LSD1 inhibitory activity, on cancer cell properties were evaluated. Isoquercitrin induced the expression of key proteins in the mitochondrial-mediated apoptosis pathway and caused apoptosis in LSD1-overexpressing MDA-MB-231 cells via the inhibition of LSD1. These findings suggest that natural LSD1 inhibitors, and particularly isoquercitrin, are promising for cancer treatment.