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Materials that possess coupled magnetic and electric properties are of significant interest because of their potential use in next-generation magnetoelectric devices such as digital information storage. To date, the magnetoelectric materials that have been studied in-depth have been limited mainly to inorganic oxides such as perovskite oxides. Molecular materials are a promising alternative because their magnetic and electric elements can be combined together at the molecular level via relatively simple molecular designs. Here, we report the coupling of magnetic and electric properties through a magnetodielectric (MD) effect in a single-crystal sample, which is constructed from dysprosium(III) single-molecule magnets (SMMs). The MD effect originates from intrinsic spin-lattice coupling of the dysprosium(III) ion within the sample. This is the first observation of the MD effect in a SMM-based material, which could pave the way toward the synthesis of advanced materials that combine distinct magnetic and electric properties using molecular chemistry for use in molecular devices with nanoscale size.