Toure turned his ankle towards the end of the first half of City's friendly win against Vancouver Whitecaps and it quickly became apparent that the Ivorian would not be able to continue.
Toure had to be helped back to the City dressing room and played no further part in the game.
The injury initially looked serious, but Mancini insisted that the damage was not too bad.
"We will have to see but I hope he will have recovered in three or four days," the Italian said.
"He fell over the other player's foot and hurt his ankle, but hopefully he will be OK."