Structural hazards, airborne hazards (like asbestos or some form of toxic gas.) Any sort of hazard that could get someone into a lawsuit is a safe bet. I'm assuming you meant the museum the prison has been converted into.
I am curious what sort of story you are writing that involves Alcatraz, I would think that might drive a reason for the closing if it was part of the plot. Otherwise both (all) the suggestions above seem logical, might add something like damage to the docking area caused by a wayward barge.
It's a bit of a sci fi thing where it's revealed that prisoners were experimented on and have kept in a secret level of the prison and something happens that finally breaks them free. The governement steps in and my only problem is making it beleivable since pretty much all the experiments are still alive even though it's been decades I think saying they were hibernating would be a good explanation but not sure. Essentially the Island gets quarantined and is closed off to the public while the good guys (soldiers sent by the government) fight off the monsters in a DOOM fashion story line.
I don't know whether you have visited Alcatraz, if not and you are able to, it would be well worth going if you are basing your novel on there, as there are so many areas that 'experimentee' could take over, move between, on the island, not just in the prison. It's an amazing setting for your story outline. I would be keen to see your progress on this one.
Alcatraz is right on the San Andreas fault. A sufficient earthquake could damage the structure to such a point that it'd be unsafe.
if there's been experiments you could say that they have found "beings/animals that would pose a significant risk to human life." and use some kind of lie to cover it up