Kaepernick was wearing a pair of the brand's headphones around his neck after the 49ers 22-17 victory over the Kansas City Chiefs.
Earlier this month, the NFL prohibited players from wearing Beats by Dre brand merchandise on camera, a step meant to protect the league's partnership with Bose.
According to the league, the ban extends to preseason training camps, practice sessions and game day and postgame interviews conducted in the locker room and on the podium.
The NFL defended the ban, saying:
"The NFL has longstanding policies that prohibit branded exposure on-field or during interviews unless authorized by the league ..." an NFL spokesperson said in a statement. "They are the NFL's policies -- not one of the league's sponsors ... Bose is not involved in the enforcement of our policies."
The league's deal with Bose replaces one it had with Motorola to supply the headsets found on the sidelines of every game. Motorola's agreement was reportedly worth $40 million per year over 13 years.
Some players have been critical of the league's enforcement of the policy.
So far this season, Kaepernick has completed 64.7 percent of his passes for 1,113 yards. Kaepernick has thrown seven touchdowns and four interceptions.
The 49ers, currently 3-2 and third in the NFC West, play the Rams in St. Louis on Monday night.
- Christopher Woody