If you are fasting for a religious issue. Then I would have to ask what religion are you in order to give you accurate information.
If you are doing it as a cleaning of your body. You should be find since even if you do bleed a little normally you rinse and spit.
And finally if you are fasting to lose weight then I would have to say that a poor died will damage your teeth in the long term. So you may want to rethink that.
Good luck to you