The actor wrote on Twitter: “I acted inappropriately toward Ms. Burton and I sincerely apologize”.
Affleck was apparently referring to his appearance on MTV show Total Request Live in 2003, presented by Hilarie Burton.
It comes after the 45-year-old had responded to the sexual harassment claims against film producer Harvey Weinstein.
The actor worked with Weinstein on Good Will Hunting, the Oscar-winning film which made the actor a household name.
Affleck tweeted that the allegations made him “sick”.
One Twitter user then commented that Affleck “should’ve just kept quiet”, and another wrote: “He also grabbed Hilarie Burton’s breasts on TRL once. Everyone forgot though.”
Burton then replied directly to the comment: “I didn’t forget”.
She then posted a video of outtakes from the show in which she appears to describe Affleck tweaking her chest during her interview with him.
Apparently talking about Affleck, Burton says: “He comes over and tweaks my left boob”, demonstrating someone squeezing her chest as she talks to the camera.
A few seconds later in the sequence Affleck asks her: “How old are you, 19?”
Burton, who acted in US teen series One Tree Hill, says she was 21 at the time.
She captioned her tweet containing the video: “Girls. I’m so impressed with you brave ones. I had to laugh back then so I wouldn’t cry.”
On Tuesday, actress Rose McGowan branded Affleck a “liar” over his statement condemning Weinstein’s “unacceptable” actions, claiming he already knew about the allegations.
McGowan says she was assaulted by Weinstein in a hotel room during the Sundance Film Festival in 1997.