Jones was criticised by sporting director Horst Heldt following Saturday's 3-3 Bundesliga draw at Hoffenheim, in which Jones' error almost presented the hosts' Roberto Firmino with a late winner.
Heldt told reporters after the game: "It is not part of our training program to create a one-on-one situation as the last man nearing the end of the game."
He added in Sport Bild: "We have decided that Jermaine Jones is to get time to think and will be left out of the squad for Basel."
Jones, 31, responded calmly to the news, telling Sport Bild: "It's true that the club has left me out of the squad. I'm using this chance to straighten out my meniscus.
"Regardless of what the club decided now, surgery eventually would have been inevitable because of the persistent pain."
An operation on the troublesome knee could see United States international Jones ruled out for around six weeks.