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The positive test violated Major League Baseball's Joint Drug Prevention and Treatment Program.
Polanco's suspension will begin at the start of the 2018 season.
"We were disappointed to learn of the suspension," the Twins said in a statement. "We fully support Major League Baseball's policy and its efforts to eliminate performance-enhancing substances from our game."
Polanco, 24, batted .256 with 13 homers and 74 RBIs last season when the Twins made the playoffs for the first time since 2010.
The Dominican Republic native said he didn't knowingly take the banned substance and had asked his personal trainer for a "combination of vitamin B-12 and an iron supplement."
"To be clear, I did not intentionally consume this steroid," Polanco said via statement released by the Players' Association. "I now know, however, that my intention alone is not a good enough excuse and I will pay the price for my error in judgment. ... I take full responsibility for what is in my body."
Minnesota will look at Eduardo Escobar, Ehire Adrianza and Erick Aybar as possible replacements.
--Field Level Media