The league said Turkoglu violated the NBA/NBPA Anti-Drug Program by testing positive for the anabolic steroid methenolone.
Turkoglu will forfeit his pay during his suspension, which was to begin with the Magic's game against Atlanta Wednesday night.
Turkoglu said he took the steroids, not realizing they were a banned substance.
"While I was back home in Turkey this past summer, I was given a medication by my trainer to help recover more quickly from a shoulder injury," Turkoglu said in a release. "I didn't know that this was a banned substance and didn't check before taking it.
"I take full responsibility for anything that goes into my body. This was a complete error in judgment on my part and I apologize to the Orlando Magic organization, the league, my teammates and the Magic fans. I know I have let down a lot of people and I am truly sorry for my mistake."
The 33-year-old Turkoglu, who is in his 13th year in the NBA, is averaging 2.9 points, 2.1 assists and 2.4 rebounds in 11 games this season. He has career averages of 11.9 points, 4.2 rebounds and 3.1 assists per game.