The genre of The Invisible Man is science fiction, or what Wells called "scientific romance." The genre is typically defined by elements of advanced scientific technology or understanding. A common feature of science fiction stories is that they often take the form of thought experiments, where the basic plot or world-building can be described as, "What if this outlandish thing happened?" In this case, the question would be, "What if a man turned himself invisible?" H. G. Wells is considered to be one of the early trailblazers in the genre of science fiction. He wrote other science fiction novels (e.g. The Time Machine, The War of the Worlds) at a time when the genre was just beginning.
The Invisible Man—and Wells's writing as a whole—was likely influenced by the popularity of children's literature in the late 19th century. Wells, along with other British authors such as Arthur Conan Doyle and Rudyard Kipling, wrote books that incorporated the action and adventure of this new children's literature into works oriented toward adults. In turn, The Invisible Man shares some things, like chase scenes, revolver stand-offs, and shenanigans, with literature oriented toward children.
In addition, The Invisible Man takes inspiration from monster fiction and ghost stories. Griffin is frequently compared to a ghost. For example, Mrs. Hall thinks the furniture that Griffin moves after he divests of his clothing is the work of spirits. Griffin is similarly creepy, being able to rob and harm while being unseen.
Finally, the novel also takes quite a bit of inspiration from Frankenstein, which also features a power-hungry scientist dealing with the aftermath of a hasty decision to go against an aspect of human nature.