Toure suffered the setback in the first half of Sunday's 3-2 loss to Liverpool at Anfield. Toure hit a strike from distance and landed awkwardly. He remained on the field but was noticeably struggling and limped off the pitch in the 19th minute.
"Maybe it's not as bad as we thought at the beginning but he needs at least 10 days or two weeks to recover," Pellegrini said.
Toure, an Ivory Coast international, will miss Wednesday's match against Sunderland at the Etihad stadium, as well as matches against West Bromwich Albion and Crystal Palace.
Sunday's defeat against Liverpool leaves the Citizens in third place in the Premier League, seven points behind the league-leading Reds, with six games to play.