State Route 586 (SR 586, OH 586) is a north–south state highway located in the central portion of the U.S. state of Ohio. The highway's southern terminus is at a T-intersection with State Route 146 in the unincorporated community of Nashport. The highway's northern terminus is at a Y-intersection with State Route 13 in Mount Vernon.

Along its way, State Route 586 travels through northwestern Muskingum County, northeastern Licking County and southeastern Knox County. No portion of this highway is included as a component of the National Highway System, a network of routes identified as most important for the nation's economy, mobility and defense.

1939 served as the year of inception for State Route 586. It was established along the routing between State Route 146 in Nashport and State Route 13 in Mount Vernon that it utilizes today. No changes of major significance have taken place to the highway since its debut.