The centre-back missed the 4-1 win over Newcastle United last Saturday after aggravating a thigh problem while on England duty, with Mourinho later blasting Three Lions boss Gareth Southgate for allegedly allowing Jones to receive six painkilling injections in order to start the friendly against Germany.
Jones missed training before United travelled to Switzerland and Mourinho expects him to sit out both the match at St. Jakob Park and the visit of Chris Hughton's side in the Premier League on Saturday.
The United boss confirmed the news at a media conference on Tuesday, describing Jones' problem as "a proper injury".
He also revealed that Bailly, another to miss training before the squad departed Manchester, will miss the Basel match but "has a chance for the weekend".
Mourinho added he hopes Chris Smalling does not earn a recall to the England squad as he wants the defender to stay fit while two of his first-choice players are sidelined.
The former Fulham man was left out of the squad this month after Southgate cast doubt on his ability to distribute the ball from the back.
"I hope he doesn't get his spot," said Mourinho. "Our injuries are real injuries. Jones does not play [on Wednesday] and I can say in advance he doesn't play at the weekend, too.
"Smalling is playing all the time and well. We don't have Jones, we don't have Eric Bailly again, so Smalling has to play every match and well, that we can say."
He added of Smalling's hopes of going to the World Cup: "Of course. I say in a selfish perspective but is not a real perspective, because what I want is my players to be happy and go to the national teams and an event like the World Cup.
"I know that, if England reach the final of the World Cup, a few weeks after we start the Premier League so I know if England goes to the World Cup final I have to start without my players but even so for England, a country I work and live in, and probably will for many years, I would like that to happen."
Mourinho added that Zlatan Ibrahimovic will be on the bench for Wednesday's game, the striker having made his comeback following knee surgery in the win over Newcastle.
"Zlatan goes on the bench and normally he plays," he said. "He needs to play and he's useful for us. He keeps the ball. If the team isn't winning, his presence will be important.
"Instead of 15, he may play 20 or 25 minutes, but he's not in condition to start."