The 25-year-old right-hander tested positive for Boldenone, the commissioner's office said Monday. Boldenone is used primarily for the treatment of horses.
Colome was 1-1 with a 2.25 ERA in three midseason starts as a rookie last year.
Colome was optioned March 8 to Triple-A Durham of the International League.
"We were disappointed to learn of Alex Colome's violation of Major League Baseball's Joint Drug Prevention and Treatment Program," the Rays said in a statement.
"We fully support Major League Baseball's policy and its efforts to eliminate performance-enhancing substances from our game."
Colome, a native of the Dominican Republic, reached the majors for the first time last season, defeating the Miami Marlins in his debut on May 30. He was recalled again in June, making two starts against the New York Yankees and Detroit Tigers before hurting his pitching elbow.
Colome was viewed as valuable rotation depth in light of an offseason elbow surgery that will keep right-hander Jeremy Hellickson out until May.
He is the second player suspended this year under the big league drug program following Yankees third baseman Alex Rodriguez, who was banned for the entire season for violations of the drug agreement and labor contract.