I thumbed through The Frogs (Aristophanes) at a used book store once. This play was written circa 400 BC. In the prologue, one character is offering to entertain the audience with a few jokes, and another character says, "Yes, but not 'That's what she said.'" The joke was too over-used.
I was astounded to think that the joke was that old! But it's actually not. The old jokes of ancient Athenians were a little too obscure, I guess, so the translator picked a modern example. Still, that translation of The Frogs is from the 1950s, so the joke was old at least that far back. (Here is the translation: https://archive.org/stream/in.ernet.dli.2015.65406/2015.6540...)