There really was a record called “Three Minutes of Silence”, and it was not so much a joke as a tribute to how ubiquitous and popular jukeboxes once were.
Sometimes in a crowded bar or restaurant, you’d be willing to pay money for just a few minutes of relief from the constant music.
You could choose “Three Minutes of Silence” and, for a nickel, actually get enough quiet time to think or talk to your date.
Pretty smart on the part of the jukebox makers, you had to pay money if you wanted to hear music, and you had to pay money if you wanted a break from it.