Salem Township is one of the twenty-five townships of Muskingum County, Ohio, United States. The 2000 census found 830 people in the township, 703 of whom lived in the unincorporated portions of the township.
Located in the northeastern part of the county, it borders the following townships:
- Adams Township – north
- Monroe Township – northeast corner
- Highland Township – east
- Union Township – southeast corner
- Perry Township – south
- Washington Township – southwest
- Madison Township – northwest
The village of Adamsville is located in northwestern Salem Township.
By the 1830s, Salem Township had a gristmill, a saw mill and two churches.
The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1. Two are elected in the year after the presidential election and one is elected in the year before it. There is also an elected township fiscal officer, who serves a four-year term beginning on April 1 of the year after the election, which is held in November of the year before the presidential election. Vacancies in the fiscal officership or on the board of trustees are filled by the remaining trustees.
The trustees elected in 2005 are Max Fox and Larry Wisecarver, and the trustee and clerk elected in 2003 are Samuel Mitchell and S. Dean Reed.