Objection 1. It would seem that God cannot annihilate anything. For Augustine says (QQ. 83, qu. 21) that "God is not the cause of anything tending to non-existence." But He would be such a cause if He were to annihilate anything. Therefore He cannot annihilate anything.
Objection 2. Further, by His goodness God is the cause why things exist, since, as Augustine says (De Doctr. Christ. i, 32): "Because God is good, we exist." But God cannot cease to be good. Therefore He cannot cause things to cease to exist; which would be the case were He to annihilate anything.
Objection 3. Further, if God were to annihilate anything it would be by His action. But this cannot be; because the term of every action is existence. Hence even the action of a corrupting cause has its term in something generated; for when one thing is generated another undergoes corruption. Therefore God cannot annihilate anything.
On the contrary, It is written (Jeremiah 10:24): "Correct me, O Lord, but yet with judgment; and not in Thy fury, lest Thou bring me to nothing."
I answer that, Some have held that God, in giving existence to creatures, acted from natural necessity. Were this true, God could not annihilate anything, since His nature cannot change. But, as we have said above (Question 19, Article 4), such an opinion is entirely false, and absolutely contrary to the Catholic faith, which confesses that God created things of His own free-will, according to Psalm 134:6: "Whatsoever the Lord pleased, He hath done." Therefore that God gives existence to a creature depends on His will; nor does He preserve things in existence otherwise than by continually pouring out existence into them, as we have said. Therefore, just as before things existed, God was free not to give them existence, and not to make them; so after they are made, He is free not to continue their existence; and thus they would cease to exist; and this would be to annihilate them.
Reply to Objection 1. Non-existence has no direct cause; for nothing is a cause except inasmuch as it has existence, and a being essentially as such is a cause of something existing. Therefore God cannot cause a thing to tend to non-existence, whereas a creature has this tendency of itself, since it is produced from nothing. But indirectly God can be the cause of things being reduced to non-existence, by withdrawing His action therefrom.
Reply to Objection 2. God's goodness is the cause of things, not as though by natural necessity, because the Divine goodness does not depend on creatures; but by His free-will. Wherefore, as without prejudice to His goodness, He might not have produced things into existence, so, without prejudice to His goodness, He might not preserve things in existence.
Reply to Objection 3. If God were to annihilate anything, this would not imply an action on God's part; but a mere cessation of His action.
Source: Summa Theologica (New Advent)