Liga - Real without midfield trio for opener
Mourinho said Sahin had picked up a new injury on top of the knee problem he was already suffering.
German international Khedira was still recovering from a thigh problem, while Altintop, signed along with Sahin in the close season, had not shaken off a bad back.
"It's not an aggravation, it's another different injury but he is not fit to play," Mourinho said of Sahin.
"I can't be more specific than that, or I don't want to be, I'll leave that up to the club's medical staff," the Portuguese added.
Mourinho did not address the controversy surrounding Real's Spanish Super Cup defeat against bitter rivals Barcelona, when television pictures showed he stuck a finger in the assistant Barca coach's eye during a mass brawl.
The Spanish football federation has opened an investigation into the incident and Mourinho could face a multi-match ban.
Looking ahead to the Zaragoza game, he said the first match of the season was always tough.
The La Liga campaign is starting a week late after the players' union called a strike over unpaid wages that was only called off on Thursday.
"Championships often start with surprises and playing away from home is always difficult no matter who the opponent is," Mourinho said.
"Zaragoza is difficult, they have one of my favourite coaches" in Mexican Javier Aguirre, he added.
"They are a very well-organised team which knows perfectly how to go on the counter-attack."
Former Porto, Chelsea and Inter Milan manager Mourinho has typically been more successful in his second season and he said he believed his Real team were better than last year, judging by their performances in the Super Cup and the pre-season.
"They (second seasons) are usually better but that doesn't mean it always has to be like that," he said.
"Let's see what happens but for the moment I have the feeling that we are playing better than last year."
The scheduled first round of matches, including Real at home to Athletic Bilbao, will be played in January.