The actor was accused of “grabbing” Burton’s breasts when they appeared together on American TV show TRL in 2003.
Batman star Affleck faced a barrage of criticism on social media after he commented on the sexual allegations made against producer Harvey Weinstein from a number of women in the film industry.
The groping claim involving Burton resurfaced when a Twitter user wrote, in response to a tweet about Affleck’s statement: “He also grabbed Hilarie Burton’s breasts on TRL once. Everyone forgot though.”
Burton then responded directly: “I didn’t forget.”
The Twitter user said they were “so sorry that happened” to Burton, to which the actress replied: “Seriously, thank you for that. I was a kid.”
Burton also shared a video snippet that appeared to show the incident and wrote: “Girls. I’m so impressed with you brave ones.
“I had to laugh back then so I wouldn’t cry. Sending love.”
Affleck tweeted, hours after her online posts: “I acted inappropriately toward Ms. Burton and I sincerely apologize.”
On Tuesday, as the furore surrounding Weinstein continued to grow, Affleck had said he was “saddened and angry” over the allegations.
He wrote: “I am saddened and angry that a man who I worked with used his position of power to intimidate, sexually harass and manipulate many women over decades.
“The additional allegations of assault that I read this morning made me sick. This is completely unacceptable, and I find myself asking what I can do to make sure this doesn’t happen to others. We need to do better at protecting our sisters, friends, co-workers and daughter.
“We must support those who come forward, condemn this type of behaviour when we see it and help ensure there are more women in positions of power.”
Angelina Jolie and Gwyneth Paltrow are among the high-profile stars who have accused Weinstein of sexual harassment, which has seen him dismissed from the Weinstein Company and issue an apology.
Weinstein has denied many of the allegations and issued a vehement denial over three allegations of rape which emerged on Tuesday.