The Croatian coach was sent off after 74 minutes in Wednesday's 1-0 Bundesliga loss to Bayern after shoving Sane.
The player had gone to get the ball from Bjelica near the Union bench for a throw-in. He pushed the ball out of the coach's hands and Bjelica then put his hands on the Germany international's face twice, pushing him away.
"Nenad Bjelica was banned for the next three league matches and fined 25,000 euros for unsporting behaviour," the DFB said in a statement.
Bjelica, who took over in November, will now miss his team's Bundesliga matches against Darmstadt 98, RB Leipzig and Mainz 05.
Union, who last year finished fourth to qualify for the Champions League, are currently in 15th place on 14 points, three above the relegation play-off spot.
