I heard it on this episode of Pod Damn America (timecode 57m 34s). Ken Klippenstein says he read it in a book on JFK written by Seymour Hersh (probably The Dark Side of Camelot).

Edit: Did some more digging and found this:

During a campaign trip to Southern California in September of 1963, JFK made a poolside grab for a woman’s ass and tore a back muscle. He was in so much pain that his doctors fitted him with a second, stiffer canvas brace to supplement the one he usually wore. In Dallas it was this new brace—not a poisoned dart from an umbrella, as one theory suggests—that kept Kennedy frozen upright after the first bullet hit him, a perfect target for the second, fatal shot.

So apparently the injury happened weeks before he was shot (not the morning of).