A new Broadway musical about Tupac Shakur just overcame one MASSIVE roadblock -- TMZ has learned, producers have obtained the approval of the rapper "s notoriously protective mother ... who LOVES the show.

A rep for the Shakur family tells TMZ, producers personally gave Afeni Shakur a rough preview of "Holler If You Hear Me" -- the new musical by black theater legend Kenny Leon, based on Tupac "s music.

According to the rep, Kenny wanted Afeni "s approval before proceeding with the show -- and he GOT IT ... we "re told Afeni was "ecstatic" and can "t wait for the show to premiere.

The musical isn "t about Tupac personally -- it "s a fictional story about two childhood friends in a Midwestern industrial city and their extended families.

A Broadway premiere date hasn "t been set -- but we "re told Leon plans to start casting next week.

tmz.com