Justin Bieber is wise enough to know when a gift needs givin’ … but he didn’t have a box — so he covered his junk with a guitar and jammed out a nak*d serenade for one lucky lady fan — HIS GRANDMA! 

TMZ has obtained photos of a completely n*de Biebs strumming away on his big wooden instrument … at his grandmother’s home in Toronto during Thanksgiving back in November 2012.

And why, you ask, did Bieber go ass nak*d for g-ma?

Our sources tell us JB had been staying at his granny’s house during the holiday … and slept in a little too late on Thanksgiving morning.

Bieber finally woke up after hearing family and friends stirring around the house — so he thought he’d prank ‘em … by grabbing his guitar and playing a nak*d set a la Jenny from “Forrest Gump” (‘memba that?).

We’re told birthday-suited Bieber went right up to his grandma and started belting out some impromptu lyrics … like, “I Loooove you grandmaaaa … how are youuuu … helloooo grandma.”

We’re told G thought it was pretty funny — and everyone in the home was cracking up — but granny begged the pop star to get back in his room to put some damn clothes on, stat.

Thanksgiving — they go balls out. Uncensored