After scoring on a 4-yard scramble that gave the San Francisco 49ers a 20-10 lead in the third quarter, Kaepernick pretended to pull his jersey apart from the middle of his chest, clearly imitating Newton's preferred celebration.
Kaepernick then mimicked buttoning up his shirt before kissing his biceps in what has become his trademark celebration.
Kaepernick referred to the celebration as "just a little shout out" following San Francisco's 23-10 victory in Carolina.
When asked who he was referring to, Kaepernick responded, "I think you know the answer."
Newton, who threw two interceptions in his postseason debut, did not seem amused by Kaepernick's celebration.
"It's not the first nor the last time somebody does that," Newton said before leaving his postgame news conference.
It was the fourth career playoff victory for Kaepernick, who was selected in the second round of the 2011 NFL draft with the 36th overall pick -- 35 spots after Newton was selected first overall by the Panthers.
Kaepernick indicated earlier this week that being selected 35 spots after Newton has helped motivate him, claiming that his draft spot is "not something I'll forget." The 26-year-old Kaepernick reiterated that sentiment following Sunday's game.
"I still won't forget it," he told reporters.
Niners tight end Vernon Davis said he did not mind Kaepernick's celebration and downplayed any perceived rivalry between the quarterbacks.
"I don't fault him for that," Davis said. "Look, I can't judge him. We can't judge him. He was just excited. I'm sure he and Cam are good friends. I'm sure they're close. He didn't mean any harm at all."
ESPN.com's Ashley Fox contributed to this report.