State Route 585 (SR 585, OH 585) is north–south state highway in the northeastern portion of the U.S. state of Ohio. The southern terminus of State Route 585 is at the State Route 3/State Route 83 duplex in Wooster. The northern terminus of this state route is an interchange with State Route 21 in Norton, where Wooster Road then continues to the northeast into Barberton.

The path of State Route 585 takes it through the northeastern quadrant of Wayne County and just into the southwestern part of Summit County. There are no segments of State Route 585 that are included as a part of the National Highway System, a network of highways deemed most important for the economy, mobility and defense of the country.

State Route 585 made its debut in 1969. This designation replaced what was a portion of State Route 5 up until that year, running from an interchange with the duplex of State Route 3 and what was then designated State Route 76 (now State Route 83) on the east side of Wooster northeasterly to an interchange with what was then U.S. Route 21 (currently State Route 21) in Norton. State Route 585 has not experienced any major changes to its routing since its inception.