Yes, cats can eat bananas, but is it really wise to give it to your cat?

Firstly, cats are really picky eater and most cats won't even lick a banana, forget eating. Also, giving your cat banana doesn't help in the cat's nutrition in any way. 
Secondly, if your cat is diabetic then you should avoid giving her bananas.

Despite banana being non-toxic to cats, it isn't right to feed your cat big chucks of banana. Instead, just give her a small slice from your banana. 

Use banana as an occasional treat rather than a staple food for your cat.