"I think Nike is trying to get out ahead of it and trying to do something special and I think they've done that", Woods said at the BMW Championship.
"I think it's a awful message that [Nike] are sending and the goal of them doing it, maybe there's a reason for them doing it".
On Wednesday, The New York Times published an op-ed from an anonymous "senior official" in the Trump administration titled "I Am Part of the Resistance Inside the Trump Administration".
He posted a revised version of a widely circulated campaign photo, which features a close-up, black-and-white shot of the former San Francisco 49er with text reading, "Believe in something, even if it means sacrificing everything".
Protesters burned Nike shoes, investors sold shares and some consumers demanded a boycott of the footwear and apparel maker's products after the advertising campaign launch.
Kaepernick has become a polarising figure after refusing to stand for the national anthem in 2016 in an effort to draw attention to racial injustice in America.
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Kaepernick has been without a club since opting out of his contract with the San Francisco 49ers in March of previous year.
He is now suing the National Football League, alleging team owners colluded to keep him out of the sport.
Tiger Woods endorsed Nike's latest "Just Do It" ad narrated by Colin Kaepernick with a message almost as succinct.
It is scheduled to air during the NFL's season opener between the Philadelphia Eagles and Atlanta Falcons, and celebrates Kaepernick and other athletes.
The two minute-plus spot features dozens of athletes, including tennis champion Serena Williams, basketball's LeBron James and Kenya's Olympic marathon champion Eliud Kipchoge.
This combination led to her being featured in Nike's new "Dream Crazy" commercial, which has a message that anything is possible.