The Ivory Coast defender sustained the problem late in Monday's 1-1 draw and, as a result, was ruled out of his country's World Cup qualifier against Malawi this weekend.
But the 28-year-old believes by the time the next league match, at Wigan on October 18, comes around he will have returned to full fitness.
"I am having some pains but it will be fine for me after the international break," Toure told skysports.com. "I was desperate to play for my country against Malawi because we can qualify that day there, but I could not do it.
"I would like to let City fans know we are together and I should be fine. It was a very hard kick on my Achilles but nothing is broken."