Although Mary Shelley was not particularly religious, she was writing within a culture that was deeply embedded within Christian thought. Her own social milieu was also very interested in the ancient Greek gods, albeit from a literary, rather than religious, perspective.
The first godlike feature of Victor is that he shares with the God of Genesis the act of creating a creature in his own image. In a sense, we can say that the monster is to Victor as human beings are to God.
The next parallel we see is in Victor's relationship to knowledge. In Genesis, humans are forbidden to eat the fruit of the Tree of Knowledge, as there are certain types of knowledge that are proper to God but not mortals. In trying to attain knowledge, humans are attempting to become godlike in a way that ends badly (the expulsion of Adam and Eve from Eden, for example); Victor is also shown as a character whose quest for knowledge beyond what is proper can be understood as a failed attempt to emulate God.
Finally, the very title of the book suggests that Victor is like the Greek god Prometheus who brings humans the gift of fire. In the works of Aeschylus, Prometheus also brings humans the civilized arts and knowledge. Victor, however, unlike Prometheus, has a failure of courage and does not care for his creation in the way that the original Prometheus cared for humans.