The fine is the maximum allowed under the collective bargaining agreement.
It was announced hours after Nashville beat Carolina 5-4 in double overtime Friday night to pull within 2-1 of the Hurricanes in their first-round series.
Staal was penalized at 14:05 of the second period for the trip. His penalty came 30 seconds after Warren Foegele sent the puck over the glass, putting Nashville on a 5-on-3. The Predators scored their first power-play goal of the series.
He also scored a goal at 3:31 of the second that tied it 2-2.