At the battle of Helm's Deep, we have:
Quote:
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Many were cast down in ruin, but many more replaced them, and Orcs sprang up them like apes in the dark forests of the South.
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Two general possibilities: a) there are no monkeys in Arda or Middle-Earth, and that was merely a translation of an animal that is similar to it, but unknown in our real world, or even just a figure of speech by the translator who wrote it in English.
However, especially the above quote makes things quite obviously this way: there are apes, but of course not in the climate of Gondor, Rohan, or the Shire, but in the hot and dense jungles to the South, in Harad. The same would go for bananas.