The Pandora story you cite is 100% Greek. There's probably a pre-Hesiodic tradition surrounding it, but as it stands, it's not Mesopotamian.
However, there are parallels with Eve from Hebrew mythology. Both ruin a utopian world through their curiosity, causing misery and strife for humans thereafter. However, both endeavor to explain why the world is toilsome, and since the world is toilsome and women were easy targets for blame (especially in a male-dominated society), it's not impossible these are entirely independent of each other.
And even if there is some relationship between the two, the way the Greek story is told is without parallel.