The incident surfaced after he posted condemnation of Harvey Weinstein, who is facing sexual assault allegations.
One Twitter user remembered how Affleck "grabbed Hilarie Burton's breasts on TRL once" but "everyone forgot though". Burton replied: "I didn't forget."
Affleck later wrote on Twitter: "I acted inappropriately toward Ms Burton and I sincerely apologise."
A clip of the moment from TRL Uncensored was recirculated, including a clip of Burton recalling how Affleck had put his arm around her and proceeded to "tweak my left boob".