The 27-year-old actress discussed working with Streep in Season 2 of the HBO series during Monday's episode of The Tonight Show starring Jimmy Fallon.
"She's so wonderfully generous and immediately disarms you with her generosity that you sort of forget for a moment that you're working with a master of her craft... and then the cameras start rolling," Woodley told host Jimmy Kimmel.
"She is like a little kid on a set in the sense of no matter how long she's been doing this and no matter how many accolades and awards she's garnered, she just genuinely loves acting. She loves storytelling. She's a master of her craft," she said.
Woodley, who plays Jane Chapman on Big Little Lies, shared her favorite memory of Streep from set.
"We're filming Episode 6 or 7, it's the very end of the whole thing, and she comes up and it's me and Nicole [Kidman], Reese [Witherspoon], Laura [Dern], Zoe [Kravitz] sitting there. She goes, 'I wonder what this line on page three has to do with this line on page seven. Hmm.' And she walks away."
"All of us were like, 'Huh?' We go through our scripts and we're like, 'Holy [expletive]. How'd she find that? How'd she do that? How'd she connect those dots?' She just reads scripts differently than anyone I've ever known."
Streep portrays Mary Louise Wright, the mother of Celeste Wright's (Kidman) abusive late husband, Perry Wright (Alexander Skarsgard). The Season 2 premiere features a scene where Mary Louise shocks Celeste and her sons by screaming at the dinner table to express her grief about Perry's death, which Woodley taught Kimmel on The Tonight Show.
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Big Little Lies airs Sundays on HBO. Woodley previously discussed Streep on The Ellen DeGeneres Show, saying the actress is "truly next level."
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