The Gers attacker was substituted during the 4-0 Petrofac Training Cup final win over Peterhead at the weekend after sustaining the injury and he limped out of the stadium.
Forrester, 25, on Tuesday signed a three-year deal which will keep him at Rangers at least until 2019. However the injury prevents him playing in his first Old Firm game.
A statement on the club’s official website read: “It had been hoped Harry would have recovered quickly but a scan on Tuesday afternoon has revealed a hairline fracture and he will be out of action for a number of weeks.”
The news comes as a blow to the Championship title winners who have forwards Michael O’Halloran and Billy King cup-tied.
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