The club said the 25-year-old would be out for "a number of weeks".
Forrester sustained the injury in the Scottish Challenge Cup final win over Peterhead on Sunday.
Earlier this week, he signed a new contract to stay at Ibrox until 2019 after helping Rangers win the Championship.
Rangers winger Harry Forrester will miss Sunday's Scottish Cup semi-final against Celtic after a scan revealed he has a hairline fracture of the leg.