Even though I have reservations on what her Bankai actually is and does, I'll base my response on the common consensus - that Minazuki involves skin corrosion.
Unohana mastered Kaidou that can, apparently, protect her from Minazuki's effects - she can fcuking heal herself from her skin melting off her bones. Considering she can do this, are we suppose to assume that she can't heal herself from Gin's toxin?
Unohana takes this without too much trouble.