Mr Pence, who has often gone out of his way to demonstrate loyalty to the president, was attending a game between the Indianapolis Colts and the San Francisco 49ers.
Some players from the 49ers kneeled during the anthem, while some Colts wore black T-shirts with the words "We Will" on the front and "Stand for equality, justice, unity, respect, dialogue, opportunity" on the back. The players stood with their arms locked during the anthem.
He explained later on Twitter: "I left today's Colts game because the president and I will not dignify any event that disrespects our soldiers, our Flag, or our National Anthem.
"At a time when so many Americans are inspiring our nation with their courage, resolve, and resilience now more than ever, we should rally around our flag and everything that unites us.
“While everyone is entitled to their own opinions, I don’t think it’s too much to ask NFL players to respect the Flag and our National Anthem.”
Mr Trump has criticised players sharply for the kneeling protests and pressed the NFL to ban them.
"I asked Vice President Pence to leave stadium if any players kneeled, disrespecting our country. I am proud of him and Second Lady Karen,” the US president tweeted.
Eric Reid, a 49ers player who began kneeling alongside Colin Kaepernick more than a year ago, called Mr Pence's departure a "PR stunt".
"He knew our team has had the most players protest. He knew that we were probably going to do it again. This is what systemic oppression looks like," he said, according to NBC.
"A man with power comes to the game, tweets a couple of things out and leaves the game with an attempt to thwart our efforts."
The kneeling protest began last year when the former San Francisco 49ers quarterback Kaepernick took a knee in response to what he saw as growing racial inequality in the US. He later lost his professional contract and has not played since.
But last month, the movement reached fever pitch after Mr Trump attacked players during a rally in Alabama.
He provoked widespread condemnation from the sport when he said: "Wouldn't you love to see one of these NFL owners, when somebody disrespects our flag, you'd say, 'Get that son of a b---- off the field right now. Out! He's fired.'"
Players and owners reacted in fury and at games the following Sunday, entire teams linked arms or knelt beginning during a game at Wembley Stadium.
Mr Trump has refused to back down and called for fans to boycott games.
There was confusion on Sunday as CBS reported that Kaepernick had indicated he would stand for the anthem if given an NFL contract.
But the CBS reporter who spoke to Kaepernick later said: "I didn't ask him if he would sit or stand."