John Calvin Commentary 1 Corinthians 5:12

"For what have I to do with judging them that are without? Do not ye judge them that are within?" — 1 Corinthians 5:12 (ASV)

For what have I to do to judge them that are without? There is nothing to prevent us from judging these also—indeed, even devils themselves are not exempt from the judgment of the word that is committed to us.

But Paul is speaking here of the jurisdiction that belongs specifically to the Church. “The Lord has equipped us with this power, so that we may exercise it upon those who belong to his household. For this chastisement is a part of discipline that is confined to the Church, and does not extend to outsiders. We do not therefore pronounce upon them their condemnation, because the Lord has not subjected them to our oversight and jurisdiction, insofar as that chastisement and censure are concerned. We are, therefore, compelled to leave them to the judgment of God.”

It is in this sense that Paul says that God will judge them, because he allows them to wander about unrestrained like wild beasts, because there is no one who can restrain their recklessness.