The star, who turned 60 last month (22Jun09), brought the accordion-like instrument with her during her appearance on Conan O'Brien's The Tonight Show - just days after a friend gave her the music box as a gift.
And Streep admits she has enjoyed irritating her husband, sculptor Don Gummer, with her attempts to master the instrument - after he gave her a toaster as a birthday present.
She laughed, "He gave me a toaster. He likes his toast. And I got this from my friend Joe Grifasi, who's an actor, who enjoys driving my husband crazy. This is a concertina. I call it 'Tina. I got it Wednesday (22Jul09). I've picked it up pretty fast.
"It's sort of amazing, it sounds like breathing and I already wrote a song. You know the greek myth about the sirens - the greek women who lure the sailors onto the rocks? This is called Siren Song.
Struggling to play the two-note tune, she laughed, "I'm sorry, it's a beautiful thing. Too bad I can't play it!".