Madison Township is one of the fourteen townships of Perry County, Ohio, United States. The 2020 census found 1,367 people in the township.

Perry County is a county located in the U.S. state of Ohio. As of the 2020 census, the population was 35,408. Its county seat is New Lexington. It was established on March 1, 1818, from parts of Fairfield, Washington and Muskingum counties. The county is named for Oliver Hazard Perry, a hero of the War of 1812. Perry County is included in the Columbus, OH Metropolitan Statistical Area. One of the poorest counties in the state, this is where the lawsuit challenging Ohio's school funding system, DeRolph v. State, began.