I'd go with supernatural, too. The MC version also says "Only cure disease or a similar spell can negate the effects."
To be honest, it's pretty close to mummy rot, minus the Cha damage. And I'll modify it a bit since it has to be modified a little anyway... How about this?
Kala Wasting/Death/Breath? (Su): Supernatural disease - inhaled, Fortitude DC X, incubation period 1 day; damage 1d6 Con. The save DC is Constitution?-based.
Unlike normal diseases, kala XX continues until the victim reaches Constitution 0 (and dies) or is cured as described below.
Kala XX is a powerful curse, not a natural disease. Conjuration (healing) spells other than remove disease have no effect on the afflicted character. Only a remove disease spell can cure kala XX (the casting character must succeed at a DC X caster level check or the spell has no effect) to cure the disease.
EDIT: that said, I could see going with the break enchantment/remove curse route like mummy rot, too.
I'd definitely add break enchantment and remove curse. The AD&D Kala's disease is a lot less lethal than mummy rot (only 1d6 hits per day), so I'd like to lower the Constitution damage - maybe 1d3?