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Found it! It's in Book IV of his Physics. The main argument is in paragraph 8, 214b13-217b28. Looking over it quickly, his argument seems to be that if there were a void, an object falling in it would have an infinite velocity. This is impossible, therefore, there is no void. As far as I can tell, he never actually says "Nature abhors a vacuum," but that might be somewhere else.
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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