Clarke, 22, will begin serving his suspension without pay at the start of the 2013 season.
The left-hander from Kitchener, Ontario was Cincinnati's 19th-round pick in the 2009 Draft out of Forest Heights Collegiate Institute and appeared in one game this season with the Reds' Rookie-level Arizona League affiliate.
Clarke, who pitched two innings on June 24, reached Class A Dayton last season, where he went 3-2 with a 2.81 ERA in nine outings, including six starts. At the time of his suspension, he was listed on Dayton's disabled list.
Players are typically issued a warning following a first positive test for a drug of abuse, followed by a suspension for a second offense. Substances considered "drugs of abuse" by Major League Baseball include cocaine, marijuana, heroin, LSD, ecstasy and other opiates. Minor Leaguers who test positive for a performance-enhancing substance are subjected to an immediate 50-game suspension.
Clarke is the 95th player to be suspended in 2012 for violations of the Minor League Drug Prevention and Treatment Program. Three of the last four suspensions have been given to Reds farmhands, with all three coming from Class A Dayton's roster.