And Streep's statement followed criticism that leading Hollywood figures had maintained a "deafening silence" in the wake of the allegations against Weinstein surfacing in the New York Times on Friday.
Streep said she wanted to make it clear that "not everybody" had known about the allegations, including herself.
The three-time Oscar-winner said the news had "appalled those of us whose work [Weinstein] championed, and those whose good and worthy causes he supported."
Streep worked with Weinstein on such films as The Iron Lady and August: Osage County and jokingly referred to him as "God" in a 2012 acceptance speech.
"Harvey supported the work fiercely, was exasperating but respectful with me in our working relationship, and with many others with whom he worked professionally," Streep wrote.
"I didn't know about these other offences: I did not know about his financial settlements with actresses and colleagues; I did not know about his having meetings in his hotel room, his bathroom, or other inappropriate, coercive acts.
"And if everybody knew, I don't believe that all the investigative reporters in the entertainment and the hard news media would have neglected for decades to write about it."
She added: "The behaviour is inexcusable, but the abuse of power familiar. Each brave voice that is raised, heard and credited by our watchdog media will ultimately change the game."
Speaking earlier on Monday, Britain's Emma Thompson said she was pleased the story had come out and described Weinstein as "a predatory man".
"We need to talk about how we're behaving," the actress and screenwriter told the BBC. "Male predatory behaviour is everywhere, not just in the film industry.
"Speaking out is the only way we'll tackle it. Let's support those women who don't have the confidence to speak out."
Some male stars have also spoken out to denounce Weinstein and express support for the women he is alleged to have abused.