The Ivory Coast star limped out of Sunday's 3-2 defeat at Liverpool 19 minutes in - shortly after shooting off-target and appearing to tweak a muscle.
Toure, 30, was initially all but ruled out of playing again this season, so the news will come as a boost to City as they attempt to overhaul Liverpool at the business end of the Premier League campaign.
The Manchester City Twitter feed quoted manager Manuel Pellegrini as saying of Toure: "Yaya has a muscle injury and we'll see how it is. Maybe it's not as bad as we thought at the beginning but he needs at least ten days or two weeks to recover."
Better news for the Chilean comes in the forms of captain Vincent Kompany and star striker Sergio Aguero, who both came through the game at Anfield with no adverse reaction to recent injuries.
The 2012 Premier League champions play host to bottom-placed Sunderland on Wednesday evening at the Etihad Stadium, and Pellegrini is expected to name both in his starting XI.
Pellegrini said of the pair: "Vincent is fine - he is on the squad list for tomorrow and so is Sergio. We'll see tomorrow who starts. It's important we start with the same high performance we showed in the second half of the Liverpool game."
On a thrilling title race in prospect, Pellegrini added: "There are still six games for us to play. The important thing is that we win our games because we can do nothing about the other teams.
"We can do a lot of things here and I'm sure the players know exactly what they have to do. They know that that starts tomorrow in winning one of the two games postponed so both Liverpool and Chelsea can feel that we are just four points and three points behind them."