Note: When it comes to the origins for certain popular idioms, well, they are not known. Usually, then, I'll mention a theory or two as to how an idiom may have originated, or, if I don't do that, then I'll at least try to include the earliest known quote of a phrase in writing. These quotes that you'll see generally come from books or newspapers, and they can give an idea for how old a saying is. So, just to give you an example, if I quote a newspaper from 1701 because a particular expression is printed in it, then the expression is at least that old. Obviously, though, if the expression is printed in a newspaper, then it's probably already a known one at that point in time, and is thus older.
KnowYourPhrase.com - Common Phrase Origins - Sayings and Their Meanings
There is an older form of this expression that goes: "Care killed the cat." The word
'care,' in this case, seems to be defined as "worry" or "sorrow." This form of the
expression goes back to at least the 16th century. It's used by a few playwrights
during that time. For example, an English playwright named Ben Jonson is said to
have used it in a play called Every Man in His Humour, 1598. Another playwright,
William Shakespeare, used the expression in the play Much Ado About Nothing, which is thought to have been written in 1599:
"What, courage man! what though care killed a cat, thou hast mettle enough in thee to kill care."
The earliest that I could find of the modern phrase being used in writing is from a book by James Allan Mair called Proverbs and Family Mottoes, 1891, where it's simply listed as a proverb on one of the pages:
"Curiosity killed the cat."
* My boss warned me that curiousity killed the cat after I kept pestering him to tell me why he fired his last employee.