The 37-year-old star - who shot to fame aged just seven in 'E.T. the Extra-Terrestrial' and was admitted to rehab when she was 13 - "appreciates" her journey to stardom, but she doesn't want hers and husband Will Kopelman's four-month-old baby Olive to have the same "exposed" childhood she did.
Speaking in the March issue of Harper's Bazaar magazine, Drew said: "I had such an exposed childhood. I appreciate my journey, but I don't want that for my kid. Not any of it.
"It has nothing to do with whether I liked my childhood. I really did. But as a parent, that isn't the childhood that I'd provide.
"Because I live my life in the public eye, I didn't want that for her. I know she didn't sign up for that.
"Unless I move into a bunker underground, I don't have a choice in this matter. It was something that took me weeks to cope with."
Drew - who was previously married to Welsh bar owner Jeremy Thomas and comedian Tom Green - is expanding her career by releasing her first make-up line 'Flower', named after her production company Flower Films.
The brunette beauty hopes her new products will be different from other beauty campaigns and she has kept the advertising raw and simple.
She explained: "I grew up in a make-up chair, and to see the women around me getting ready was so aspirational. It's about mothers and daughters, a girl watching her mom at a vanity table.
"I didn't want a cold campaign with severe messaging. I wanted warmth and acceptance and self-love. Nobody's in gold rain or running through a jungle with their lipstick on.
"It was just me and some great music on a white background. That's every girl, in her closet getting ready."