The incident occurred in the second quarter of the teams' clash last week.
Kaepernick was running out of bounds and had reached the sidelines when Matthews came in with a hit to bring him down.
This started a melee between the two sides and Matthews then slapped offensive lineman Joe Staley as he defended his quarterback.
After reviewing the footage from the game, the NFL have deemed that the linebacker is worthy of a hefty fine for the tackle.
Green Bay face the Washington Redskins on Sunday.