The cat's owner, Carol Kowalewycz, said she does not know how it happened or why, but she thinks somebody did this on purpose.
"I'd like people to know that somewhere in this neighborhood, there's somebody that's not very nice," she said. "I really fear for all the other animals and maybe the children."
The arrow became lodged in the cat's head, but missed its brain and ear canal. The cat - known as Mama Cat - is expected to make a full recovery.
Mama Cat had an emergency surgery on Wednesday night and was able to come home Thursday afternoon.
The cat will be on pain medication while it recovers.
Kowalewycz said she hopes somebody will come forward with any information about her pet's injury.