Magnetodielectric response mechanisms are critical for the rational design and synthesis of molecule‐based magnetodielectric materials. Herein, the magnetodielectric response was investigated in the molecule‐based material [Fe3O(CH3COO)6(py)3](py) (1). Its magnetodielectric coefficient (MD) is −2.8 % for phase transition III and −4.1 % for phase transition I. Study of the mechanism of the magnetodielectric response in 1 reveals that its magnetodielectric response at phase transition I is induced by the charge‐frustration of the trinuclear iron cluster, while that at phase transition III is attributed to the spin‐frustration of the trinuclear iron cluster, providing a new route for the design of magnetodielectric materials.