The 14-year-old Stranger Things actress joins Prince Harry, Meghan Markle and rapper Cardi B on the 2018 list.
She is the youngest person to be included in Time's top 100, which is published every year.
Brown rose to fame with her role as the character Eleven in the hugely popular science fiction TV show. She starred in the first series when she was 12.
Other famous figures who made the Time magazine list include singers Rihanna, Kesha and Shawn Mendes as well as US President Donald Trump and North Korean leader Kim Jong-un.
Tennis player Roger Federer, actress Nicole Kidman and Scottish Tory leader Ruth Davidson also feature among the 100 along with Mayor of London Sadiq Khan.
Writing an appreciation of Brown for Time magazine, US actor Aaron Paul called her an "extraordinary" actress.
"She may have been 12 in years, but her spirit and mind were timeless," he said, speaking of first meeting the teenager in New York.
"A wise woman was speaking from her cherubic face.
"It was like speaking to a future mentor with a perspective and groundedness that I could only have dreamed of at that age. Or at any age, if I'm being honest."
Mr Paul added: "Maybe that's why she's such an extraordinary actor.
"She somehow understands the human experience as if she has lived it for a thousand years. I'm proud to know her. To call her a friend. To call her my adopted daughter."