The two fans will be refunded for the cost of their tickets, a source told the sports network.
On Tuesday night at Yankee Stadium, Betts leaped at the wall in foul territory and initially caught Gleyber Torres' popup in the first inning, but a fan in the first row, Austin Capobianco, grabbed Betts' glove with both hands and pulled the ball out. Capobianco's friend, John Peter, then grabbed Betts' non-glove hand.
Betts reacted angrily, and Torres was immediately ruled out by right-field umpire Mark Carlson on fan interference.
"Tonight marks the final home game of year, and we want every ounce of our fans' passion on display," the Yankees said in a Wednesday statement. "Yankee Stadium is known for its energy and intensity, however the exuberance of supporting one's team can never cross the line into intentionally putting players at physical risk.
"The Yankees and Major League Baseball maintain a zero-tolerance policy toward the type of behavior displayed last night. These fans will not be permitted to attend tonight's game in any capacity."
Capobianco, a Yankees season-ticket holder, said he knew he would be in trouble but chose to grab and open Betts' glove nonetheless, telling ESPN that he and Peter often discuss this exact scenario: If a foul ball comes their way, they're going to do what they can to help their team.
"We always joke about the ball in our area," Capobianco, 38, said at a local bar after the game. "We're not going to go out of our way to attack. If it's in our area, we're going to 'D' up.
"Someone defends, someone knocks the ball. We talk about it. We're willing to do this."
Betts, who was visibly frustrated in the moment, downplayed the incident after the game.
"When it comes to the person in play, it doesn't matter," Betts said. "We lost. It's irrelevant. I'm fine. He's fine. Everything's cool. We lost the game and that's what I'm kind of focused on. We got to turn the page and get ready for tomorrow."
The Dodgers had a two-run lead at the time on Freddie Freeman's two-run homer, but the Dodgers were unable to complete a sweep and took an 11-4 loss to the Yankees.
"I've never seen anything like it," Dodgers rookie pitcher Ben Casparius said. "It's pretty interesting. It was obviously very early in the game so I think it kind of set the tone."
Capobianco and Peter were escorted out of Yankee Stadium but said they were told they would be allowed back for Game 5 on Wednesday. The Yankees did not immediately respond to ESPN's request for comment regarding if that was indeed the case.
"I know when I'm in the wrong and as soon as I did it, I was like, 'Boys I'm out of here,'" Capobianco told ESPN. "I patrol that wall and they know that."
The situation was reminiscent of Game 1 of the 1996 ALCS at Yankee Stadium and the controversy that ensued, when preteen New York fan Jeffrey Maier intercepted a fly ball that seemed destined for the glove of Orioles right fielder Tony Tarasco. With no replay review at that time, the hit went for a Derek Jeter home run and became the stuff of October baseball legend.
It was the second time Torres had an at-bat affected by fan interference in this World Series. With two outs in the ninth inning of Game 1 at Dodger Stadium, Torres hit a fly ball to left field, and a fan reached over and caught the ball. Torres was awarded a double.
In Game 4, Torres later hit a three-run homer to right field for New York's final runs.
ESPN and the Associated Press contributed to this report.