This answer is essentially a re-post of my answer to the same question from the Mythology Stack Exchange.
Although Joseph Campbell is very popular with the general public, there are a number of significant flaws in his theory that people tend to ignore. To quote from Alan Dundes, a professor of Folklore and Anthropology at the University of California, Berkeley:
My sole point in mentioning this disheartening incident is to suggest that for many members of the literate public, the study of folklore means precisely Campbell and his writings. Yet professional folklorists have said very little about the huge corpus of Campbelliana. I do not know if any of his many books were ever even reviewed in JAF. Is this a case of "silence gives assent"? Very likely more people were introduced to the subject matter of folklore by the writings of Campbell or the PBS television series of lectures by him than by any other source. And yet we folklorists have said little or nothing about him and his theories.
Dundes makes a number of criticisms of Joseph Campbell. One of these is of his assumption that myths are universal, which, as Dundes quickly proves, is not the case. To quote from Dundes:
It has long been a popular fantasy among amateur students of myth that all peoples share the same stories. This is clearly an example of wishful thinking.
Examples of myths that Joseph Campbell claims to be universal but which are not are include:
- The flood myth, which is "absent from sub-Saharan Africa" (Dundes).
- The "virgin-birth" motif, which is only present in three separate myths, and is absent from "Africa... Siberia, Polynesia, ... Melanesia, ... Australia and New Guinea" (Dundes).
- The "belly of the whale" motif: this "motif" is only present in the old testament (Dundes). The only other example Campbell cites of a "belly of the wale" motif -- the story of Red Riding Hood -- is a horrible example. Red Riding Hood is only swallowed by a wolf in the written version of the story; in the oral version of the story "the girl is not swallowed by the wolf at all... Instead she escapes through a clever ruse by pretending to need to go outside to defecate" (Dundes).
I think it would be safe to say that Joseph Campbell's arguments that the monomyth is "universal" aren't very sound. If you are interested in reading more, Dundes' article is available on JSTOR, which you can usually access for free from a public library. Dundes has other criticisms of of Campbell, but they aren't relevant to the question asked by the OP.
I also recently wrote a blog post about Joseph Campbell that might interest you. It elaborates on the points that I made in this post.