The incident occurred moments after Kaepernick shoved a local CBS affiliate cameraman out of his way by the camera's lens on the way to the locker room.
The verbal altercation was captured on video and posted by TMZ Sports, as Moore seemed to be waiting for Kaepernick.
"I'm good," Moore said.
"I hope you are," Kaepernick answered. "I'm coming for you. I'm coming for you."
As Kaepernick kept walking, being led away by right guard Alex Boone, Moore continued to say louder each time, "I'm good."
Until he called Kaepernick a series of expletives.
In the game, Moore had one tackle, a seven-yard loss of Kaepernick on a designed sweep to the left. But the linebacker took a bigger swipe at Kaepernick on social media after the Raiders' 24-13 victory.
Moore posted a photo on his Instagram account of himself and Kaepernick face to face in the game and wrote, "There's a difference between boys and Men ... Freakin chump"
Kaepernick finished with a passer rating of 54.4 after being intercepted twice, getting sacked five times and taking three delay of game penalties. He was asked after the game if Moore or other Raiders players had tried to bait him after plays.
"I don't worry about things like that," Kaepernick said.