Johnson hopes to be fit within a month but City boss Roberto Mancini does not want to rush his return to the Eastlands team.
Johnson is way down the pecking order in City's star-studded midfield and the club will let him move to Elland Road in January in a loan move until the end of the season.
Leeds have reassured City that they will not ask too much of Johnson when he returns but Simon Grayson has assured Mancini that the 22-year-old will have a part to play in their promotion push.