The videos, which were filmed last year, show four dogs latching on to a man wearing an oversized red jersey bearing the name and number of Mr Kaepernick, the former San Francisco 49ers quarterback who has been criticised by Donald Trump and other conservatives and right-wing officials and media outlets for kneeling during the national anthem as a silent protest against police brutality.
Mr Kaepernik, who is black, played his final NFL game in 2017 but continues to promote civil rights causes.
"The inherent message of this video is completely inconsistent with the values and ethos of Naval Special Warfare and the US Navy," the branch said in a statement on Sunday.
Footage from the K-9 demonstration was filmed at the National Navy SEAL Museum in January 2019 but did not come to the Navy's attention until viral images circulated over the weekend. The men in the video are not believed to be service members but civilian employees or contractors.
"We are investigating the matter fully, and initial indications are that there were no active duty Navy personnel or equipment involved with this independent organisation's event," the Navy said.
A caption from one clip of the demonstration, shared to Instagram, said "for not standing during the national anthem."
In another video, the man can be heard saying "I will stand" as the crowd at the museum watches and laughs.
— Billy Corben (@BillyCorben)August 2, 2020
The Florida museum, on former naval training grounds, has hosted several other dramatic and violent demonstrations, including a hostage simulation in which women were abducted by three men in black-and-white scarves, and a military-outfitted group facing a vehicle that says "Take a Knee."
Following widespread protests against police brutality and racial injustice in the wake of police killings of black Americans in the US, Navy Admiral Michael Gilday urged officials to discuss "race relations and inclusion" within the branch.
"We must demand of each other that we treat everyone with dignity and respect," he said in June. "If you won't do that, then our Navy is not the best place for you."
That month, NFL commissioner Roger Goodell apologised for earlier comments and threats to fine players who refused to stand for the anthem while on the field, which enraged the president and his allies who claimed that it was disrespectful to the American flag and the military.
"We, the National Football League, believe Black Lives Matter," he said. "The protests around the country are emblematic of the centuries of silence, inequality and oppression of black players, coaches, fans and staff. We are listening."
In 2017, the president said: "Wouldn't you love to see one of these NFL owners, when someone disrespects our flag to say, 'Get that son of a bitch off the field right now. Out. He's fired. He's fired.'"
He has since welcomed the idea for Mr Kaepernick to return to the league, though he continues to condemn the practice of kneeling during the anthem.
"Looking forward to live sports, but any time I witness a player kneeling during the National Anthem, a sign of great disrespect for our Country and our Flag, the game is over for me!" he said last month.