The commissioner's office announced Friday that Atilano was punished following a second violation for a drug of abuse, while Duarte was disciplined after testing positive for an amphetamine. The suspensions take effect immediately.
Atilano, on the roster at Double-A Pensacola, has been on the disabled list most of the season. Drafted 35th overall by Atlanta in 2003, the right-hander went 6-7 with a 5.15 ERA in 16 major league starts for the Washington Nationals in 2010.
Duarte is a combined 2-0 with a 2.12 ERA and two saves in 15 relief appearances for Double-A Portland and Class A Salem this year. This is his first season in the Red Sox system.
There have been 49 suspensions this year under the minor league drug program.