Mr Weinstein faces charges in New York involving alleged sex assaults on two women, which he denies. He has been accused of sexual misconduct by more than 70 women and also faces additional investigations by the US federal government.
Watson, who starred in the Harry Potter films and Disney’s Beauty and the Beast, is pictured wearing a Time’s Up T-shirt in her post.
She wrote: “From my sisters in the film industry to the activists and campaigners around the world who have supported us, I’ve been so inspired by the way people have reached out to each other, shared experiences and advice, and organised together as part of this movement for change.
“Gender equality can only become a reality if we harness the transformative power of solidarity across professions and across borders.
“There’s still a long way to go, but the achievements so far make me optimistic for a fairer future. 2018 was just the beginning.”
As of December, Time’s Up had attracted $22m (£17m) in donations, and the services of hundreds of volunteer lawyers.
The campaign, which is backed by hundreds of actresses including Natalie Portman, Reese Witherspoon, Cate Blanchett, Eva Longoria, Emma Stone and America Ferrera, was announced via a full-page advert printed in the New York Times on 1 January 2018.
It is aimed primarily at those victims of sexual harassment unable to pay for legal support themselves, such as agricultural or factory workers, caretakers and waitresses.
Time’s Up also calls for “gender inequality and the imbalance of power” to be addressed, emphasising the need for more women to gain positions of authority and parity of pay.
Watson, 28, has been a prominent supporter of the organisation since its inception.