Bayern, who beat Inter 2-0 in their Champions League group opener on Wednesday, will look to bounce back after two consecutive league draws forced them off the top spot.
"King was injured in training and is currently undergoing a scan," Nagelsmann said of the France international. "It does not look too good. Hopefully it is only a muscle fibre injury and nothing even worse than that."
There was good news for midfielder Joshua Kimmich (27), who is nursing a black eye but was cleared to play, the manager added.
The German champions, currently in third place on 11 points, one behind leaders Freiburg and Borussia Dortmund, also face Barcelona on Tuesday in the Champions League, meaning Nagelsmann will be busy rotating.
"It would dumb if I ignored the Barcelona game," said Nagelsmann. "We will be rotating a bit to keep the tension high in the squad. There will be some changes."
Among those who will not start on Saturday is Leroy Sane (26), who scored once and set up the other goal against Inter.
"A break is planned tomorrow for Leroy. At least he won't start. He did considerable work against Inter," Nagelsmann added.
Jamal Musiala (19), Mathys Tel (17) and Serge Gnabry (27) were likely replacements, Nagelsmann said.
"There will be some new faces (in the team), firstly to balance fatigue but also to maintain a rhythm."
Stuttgart have yet to win a match this season, having drawn four out of five to sit in 12th place on four points.
