The man is being held in investigative custody, broadcaster n-tv reported on Tuesday.
He is accused of having been distracted by video games on his mobile phone at the time of the crash, which saw two local trains collide head-on along a single-file stretch of track outside Bad Aibling, southeast of Munich.
Official investigations have found that the controller made several "tragic" mistakes which led to the disaster.
He first allowed both trains to access the single-track line, and then when he realized his error, he pushed the wrong button and alerted other controllers.
His second signal did go to the right train drivers, but officials said it was by then too late.
After the trains rammed into one another at high speed, the final toll stood at 11 people killed and dozens seriously injured.
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