Accepting the Best Performance In A Show role her portrayal of Eleven in the Netflix series, Millie said: "Since I know there are many young people watching this — and even for the adults, too — they could probably use the reminder that I was taught: if you don't have anything nice to say, just don't say it.
"There should be no space in this world for bullying, and I'm not going to tolerate it, and neither should any of you."
She added: "If you need a reminder of how worthy you are and to rise above the hate, message me on Instagram."
Since the deletion of her Twitter account, Millie has also disabled comments on her Instagram posts.
As 'Stranger Things' has increased in popularity, there has been much discussion about the raised profiles of the show's young cast, particularly on social media.
Finn Wolfhard - who plays Mike in the show - previously spoke about this in a message addressed to the show's fans, weeks after the second series debuted last year.
"I don't wanna ex-communicate anyone from this fandom," he said. "But if you are for real you will not harass my friends, or co-workers. Y'all know who you are.
"Why I even have to tweet that, I don't know. Anyone who calls themselves a 'fan' and actively goes after someone for literally acting and doing their job is ridiculous."
He concluded: "Think b4 ya type boiiii."