Missouri's armor was penetrated by friendly fire from an escort's CIWS. I don't think it'd stand up to a full-blown antiship missile.
Sauce or it didn't happen.
EDIT:
You fail at understanding navy warfare and ship design Batutta.
Battleship, and ESPECIALLY the Iowa, are designed for redundancy and being especially hard to mission-kill.
You can turn it into a burning piece of scrap - but it will still float and fire. Fire control, ammo and the guns - heck, all mission-critical areas - are the most protected ones.
The ship will not be able to fight without the superstructure. End of story. Radar, comms, everything: it's up there.
Compare the cost of even a hundred ASMs to the cost of the Missouri, not to mention the cost of such a humiliating defeat to the US, and it's easy to see why battleships are gone.
The fact that the Yamato could be taken out by
WWII bombers and torpedo planes suggests that Missouri is going to end up just the same way in the face of a saturation ASM attack. The same is probably true of today's carriers, mind, but at least they don't have to get so close.