Bayern clinched first place in Group A, considered the "Group of Death," so it will leave the pair behind for the trip to England. Dutch international Robben just recently returned from a long injury absence, while German international Kroos has been in top form.
"I'd have liked Arjen to be with us," Bayern coach Jupp Heynckes said. "After such a long time out with injury, he needs matches."
Bayern also revealed German internationals Mario Gomez and Thomas Muller could also miss the game, as the "pair are showing early flu symptoms," according to the club's website.
Heynckes admitted he would be making a "couple of changes" regardless.
City is unbeaten and atop the English Premier League, but lost the first match against Bayern in Munich, 2-0, and needs a victory at Etihad Stadium to have a chance to advance from group play.
The English giants enter the last matchday in third place behind Bayern Munich and Napoli, which can seal its progression with a win over Villarreal.
"We can approach the game with a certain amount of calm," Bayern captain Philipp Lahm said, "but we will do everything to ensure that we come home with the points.
"We are athletes and want to win every game."