I read the article on Harry Potter Wikia, but does it work on Muggles? If an invisibility cloak somehow found its way to Muggle hands, won't the whole cover of the Magical World be blown away? Are there charms such that Muggles can't see invisibility cloaks?
It works on inanimate objects, so there's obviously nothing very specific to "only magical beings inside".
The invisibility cloak would work on Muggles, exactly like it works on everything else. It makes anything underneath it invisible.
Muggles finding an invisibility cloak would cause no bigger a problem than Muggles seeing a dragon, or Muggles seeing a wizard Apparate. If there was a danger of Muggles learning something about the magical world from finding the invisibility cloak, the Department of Magical Accidents and Catastrophes would step in and deal with the problem, likely by removing the cloak and modifying the memories of all the Muggles involved.
I thought the whole concept of Muggles and the magical world was that Muggles do see magic they just ignore or rationalize it away. The invisibility cloak being that it's a magical object would work on anyone magical or non as long as they could fit underneath it.
It works on human beings, so, in particular, it works on muggles.
Yes, the invisibility cloak would work on muggles. It is like the killing curse worked on muggles when Peter Pettigrew or he-who-shall-not-be-named used it on a muggle. If you have read the books, you would know that wizards and witches can modify memories. If a cloak was discovered, they would find the muggles that have used it, and others they have told, and modified thier memories.