Stones, 23, pulled up and grasped the back of his leg before being replaced in the 31st minute of City's 2-0 win at the King Power Stadium.
City boss Pep Guardiola confirmed after the game that the centre-back is likely to be sidelined for a month and a half.
"It is tough because the calendar is so demanding," the BBC reported quoting Guardiola.
"We don't have many central defenders and they will suffer - but we will find a solution."
City are without full-back Benjamin Mendy, who will be out for another five months after rupturing the anterior cruciate ligament in his right knee against Crystal Palace in September.
Stones was replaced on Saturday by Eliaquim Mangala, making just his fourth appearance of the season.
They were also boosted by the return of fellow centre-back Vincent Kompany, also playing his fourth club game of the season after recovering from a calf injury.
