Exum was penalized for unnecessary roughness on the play in which he hit Woods in his midsection in the third quarter of the 49ers' 48-32 loss while breaking up a deep pass.
This marks the third time this season Exum has received a fine for a hit, the other two being a $53,472 fine for a Week 14 hit on Denver Broncos receiver DaeSean Hamilton, and a $26,739 fine for a hit on Kansas City Chiefs receiver Sammy Watkins in Week 3. The $26,739 fine was reduced to $5,000 on appeal.
Exum's weekly paycheck comes out to $41,470 before taxes, meaning this is the second time he has been fined more than a weekly game check.
The Rams' Samson Ebukam was also fined $26,739 on Saturday for unnecessary roughness when he lowered his head to initiate contact on a tackle.
Miami's Kiko Alonso and Robert Quinn were docked $10,026 for unnecessary roughness, and Buffalo's Jordan Mills was fined $13,369 for unsportsmanlike conduct after they were all ejected for their roles in a skirmish between the teams last Sunday.
With Bills quarterback Josh Allen already sliding in the third quarter of Buffalo's 42-17 win, Alonso dived in front of him and kicked the quarterback in the helmet. A scuffle broke out amid a group of players, and Quinn ran in and dived atop the pile.
Dolphins safety Minkah Fitzpatrick was also fined $10,026 for unsportsmanlike conduct during a play in the fourth quarter of that game.
Chicago punter Pat O'Donnell has to pay $15,000 after he was penalized for unsportsmanlike conduct when he was on the sideline but too close to the side judge, who tripped over him and immediately threw the flag. Bears teammate Deon Bush was fined $10,026 for a face mask penalty against Minnesota.
ESPN's Nick Wagoner and The Associated Press contributed to this report.