The short answer: It is not recommended.
The long answer: Though dogs can eat bananas, it is not recommended for cats to snack on these fruits. Bananas are high in sugar and carbohydrates, which are not needed by cats to survive and thrive. As obligate carnivores, they need protein and fat to fulfill their dietary needs. Feeding your cat high amounts of carbohydrates is detrimental to her health and may result in diabetes, irritable bowel syndrome, obesity, and/or constipation.
Some cats may also be allergic to bananas. These cats exhibit symptoms such as vomiting, diarrhea, flatulence, frequent scratching or hair loss, inflamed skin, chronic ear problems, coughing, wheezing, and sneezing.
What to do if your cat accidentally eats bananas: Try to find out how much banana your cat has consumed. Keep an eye on her and report any noticeable changes to her veterinarian. If your cat ate a portion of the banana peel, this may cause a block in her respiratory or digestive systems. Also, take note of allergic reactions your cat may have after consuming the fruit.
In summary: Carbohydrates should only make up 0 to 2% of your cat’s daily diet. Since bananas are packed with carbohydrates, your cat is better off not consuming this tropical fruit. Plus, the sugar found in bananas is something her tongue cannot taste and her body cannot digest. She will be better off eating protein-rich meals and snacks made especially for her.