An online petition demanding the dumping of his cameo in 2018 heist movie Ocean's 8 has nearly reached its goal of 17,000 signatures - signed by more than 16,620 supporters by late afternoon New York time Thursday.
Critics say his inclusion would be particularly galling given its status as an all female reboot of the popular franchise, starring Cate Blanchett, Sandra Bullock, Anne Hathaway and Helena Bonham Carter.
The petition calls on Oceans 8 producers George Clooney and Steven Soderbergh, "to toss Damon's Oceans 8 cameo where it belongs: on the cutting room floor."
It alleges that he "enabled" Harvey Weinstein's conduct by trying to squash a New York Times report in 2004 that detailed instances where the now fallen Hollywood mogul exploited his status as a studio executive to harass and assault women.
Damon denied trying to bury the story and claimed he had no idea of the allegations against Weinstein, who helped catapult him into an international household name.
The actor also came under fire last week, for telling ABC News that there was a "spectrum of behaviour" and a "difference between, you know, patting someone on the butt and rape or child molestation, right?"
His long-time friend, Ben Affleck, with whom he shared an Oscar for best screenplay over 1997 movie Good Will Hunting and Affleck's actor brother Casey, have also been accused publicly in recent months of sexual misconduct.
"This behaviour is beyond enabling - it's just gross. Matt Damon should not be in this movie," said the petition.
"Damon's inclusion would trivialize the serious nature of the charges against sexual abusers like Weinstein," and "show massive disrespect" to women speaking out, it said.
Harvard-educated Damon, 47, is the father of four daughters, including a child from a previous relationship of his wife.
Ocean's 8 is scheduled for release in June 2018 and tells of an attempted heist at New York's annual Met Gala, one of the hottest tickets in the celebrity universe.
