Think smarter, not harder.
While I don't plan on press the same key again, this feel like a pointless thing given what it'd take. For starters, entropy itself is not something that can be observed, only calculated. Add to that how the effects of entropy themselves generate signals many animals can and do detect and we have a situation where the cool organ proves as a waste.
Entropy itself, if I understand correctly, manifests in our world on a macroscopic scale mainly through 3 ways: changes in temperature, changes in appearance and decomposition, and we already have examples of animal senses for all of those. Hell, in the case of changes in appearance you have at least 3 or 4 different types of eyes in the animal world to choose from.
Not long ago I answered a question about a potential new organ capable of detecting water, and my answer to that question was "they already exist in elephants, and they're called trunks". This is a similar scenario, except you want a single organ that does the job of many, and that will not only be impossible, but be potentially worse overall in a scenario where it wasn't, since forcing a single organ to detect many things means it cannot be specialized, and thus can't be as effective as a specialized one (a universal price to be paid in the animal kindgom, Jack of all trades, master of none will be more flexible than the master of one, but they sure as hell won't beat the master in their specialty). The eyes of birds let them see shades of color we never will, shades which make them able to detect what to us would've been a perfectly camouflaged rabbit. Hammerhead sharks have potent electroreceptors in their heads, which allow them to detect basically anything that uses some form of electric signal to function while it's underwater and close enough. Fun fact: those are basically present in basically every form of multicellular animal life on earth. Foxes, as far as we know, use earth's magnetic field to help them hunt prey hidden in the snow, and owls do the thing, but instead relying on asymmetrical ears and potent hearing to be able to detect the exact distance of prey from it with frightening accuracy in 3 dimensions, all that without movable ears, all while bats and dolphins simply use sound to perceive the ambient around them and move around expertly even in absolute darkness, while also be able to tell a lot about what's nearby simply based on how sound bounces off it.
In your example scenario, the goal is to forage for edible fruits. Sure, a magical entropy detector might be able to tell a more complex plant from a less complex one, but will it be able to tell which of the more complex plants is currently producing fruits? Or even if the fruits have nothing poisonous to it in them? While it struggles to figure that out, a monkey with good eyes and a better nose has already found the fruits and could tell both whether they were edible and which were the most fresh. Your entropy organ might be able to allow the creature to sense fish hidden underwater in a river... Only for an electric eel to also come along, be equally able to identify basically everything nearby with a nervous system and zap the ones it liked so it could eat them.
Summing up: could it exist? Probably not, since entropy itself cannot be measured, and even if it could, there's a pretty high chance that it would not be as effective as simply having a large number of already existing sensory organs made to identify different things, many of which are already direct effects of entropy. I get the reasoning, it sounds much cooler to say "we're being hunted by something that can sense entropy itself" in a story than "the thing hunting us has a crazy sense of smell", but the truth is that nature already provides a large array of examples on how you don't need to be able to detect every little aspect of reality to be a good hunter.
To put one last thing in perspective on what makes a good hunter: unless my memory is failing me, the most successful predator in the world is the not-so-humble dragonfly, which can basically catch what it's after 97% of the time. How does it do this? Pristine eyesight and motion detection helps a lot, but being able to use said eyesight to predict where its prey will go helps even more. What it can perceive is only a portion of what makes something successful. How it uses that available information is arguably much more important, especially since koalas are here to demonstrate just that.