I don't refrigerate my bananas - and I've been wondering whether I should do. So who to ask? Well let's see what AI says:. "Yes, bananas can be refrigerated, but it's best to do so when they are fully ripe.". Then the question becomes, what is "fully ripe"? "When they are fully yellow and started to develop brown spots." OK. Of course, I only buy enough bananas in one go so that I can consume them before they become overripe. So all of this is rather redundant.