The word comes from discotheque, of course, which has been around in the French language for a looooong time.
But it’s introduction into American vernacular seems to hark back to a First Mention in this Time magazine article from July 5, 1963 which gives a pretty good definition, to boot (sans music):
|Warfield’s arena was the doll-house dance floor of the exclusive Princesse, one of the 50 discothèques that currently preside over Parisian night life. La Princesse is a definitive discothèque—a private-unless-we-know-you bar that is smoky, chic and expensive.|
1963. John Travolta was nine years old, and the Bee Gees didn’t exist yet, but there you have it…the discotheque was introduced to a US audience.
You can read the full Time Magazine article here.