The midfielder has been suffering the problem for two weeks, while David Silva will also miss out against Blackburn Rovers on Wednesday
The 30-year-old has scored 10 goals in 20 Premier League appearances this season as City sit one point behind leaders Arsenal in the table.
Pellegrini’s men face an FA Cup third-round replay against Blackburn Rovers on Wednesday evening but the Chilean has confirmed Toure will be rested for the fixture.
"David Silva and Yaya Toure are (out) with small problems," Pellegrini said. "I hope they will be fit for Saturday.
"Yaya has the last two weeks played with a problem with his back, so it is a risk to continue doing that way. It is better for him to rest for two or three days."
Pellegrini has confirmed Sergio Aguero has returned to full training after suffering a calf injury in December and will be available to play against Blackburn.
"Sergio is working normally with the whole squad and he is in the squad list,” said the City manager.
"He is a very important player for us. It doesn’t matter that we are scoring a lot of goals. Sergio will always will be an important player. We are very happy he is coming back."