"Has the cat got your tongue?"
Would you be surprised to hear that no one really knows?
There are suggested origins, such as the one from language maven Richard Lederer, who offered this explanation: "The anticipation of a beating by the cruel cat-o'-nine-tails, often shortened to the cat, could paralyze a victim into silence. That's why 'Has the cat got your tongue?' came to mean 'Are you unable to speak?'" (Mr. Lederer is the host of "A Way With Words," on KPBS, San Diego Public Radio.)
But Evan Morris, author of the Word Detective website, says “the most surprising thing about ‘cat got your tongue’ may be its relatively recent vintage. While it certainly sounds as if it must have been dreamt up back in the Middle Ages, the earliest written example listed in the Oxford English Dictionary is from 1911.”
(sorry, bad pun)
Sources: Grammarphobia and Jewish World Review