The four-year veteran received a roughing the passer penalty in the fourth quarter of last Sunday's 35-14 Giants victory.
The New York Times reported receiving an e-mail message from Randall Liu, the information manager for the National Football Conference, stating that Tuck was fined because "he unnecessarily drove the opposing quarterback to the ground."
During a pass attempt, the 6-foot-5 inch, 274-pound Tuck launched himself at Bollinger then drove him full force into the ground.
He told the newspaper that he would appeal.
"You can't hit (the quarterback) in the head, (and) you can't hit him below the knees," Tuck told the newspaper. "Obviously, you can't hit him hard, either."
Tuck recorded 2 ½ sacks in the contest, and with 8 ½ sacks in eight games, he leads the Giants defense.