The grammatical rule is il faut + infinitive verb.

In your example, Il me faut le faire uses faire as a complementary infinitive (l’infinitif complément) of another verb, il faut. Il faut (verbe falloir) takes the infinitive without a preposition to express "It is necessary (for me) to do (it)."

This is not an exception; il faut does not take a preposition before the infinitive.

If the subject changes for emphasis/style, you can use il faut with que (relative pronoun, not a preposition) followed by the subjunctive. That would rephrase your sentence to Il faut que je le fasse, but this would change the register. Using the infinitive helps avoid the subjunctive in this way, but it’s more common/colloquial in speaking to use the subjunctive for such a short expression than the complementary infinitive with the pronouns. I would expect to see that more in writing.

This Ngram shows how much more common it is to say "il faut que je le fasse," but that doesn’t change the grammatical rule of il faut + infinitive without a preposition.

Some other verbs that work this way like valoir, aller, devoir, aimer followed by an infinitive are given here as well as a list of some verbs that do take a preposition.