How old is the cat? Feline adult canine teeth come in at about 5 months. Is it the adult tooth coming in? If it's a deciduous canine tooth, what's left of the root may just fall out when the adult tooth comes in.
If the tooth is broken, then it needs to be repaired, just like it was in your mouth. If the tooth was totally knocked out, then the injury site at least needs to be treated for infection. Cat's have filthy mouths teaming with all sorts of bacteria.
If it was one of my girls, then I would have taken her to the vet already.