The England Under-21 international was forced off after 20 minutes and went straight to hospital for an X-ray which confirmed the fracture.
Cranie signed a three-month loan deal on October 8 and has played an important part in Rangers' recent revival - making five impressive appearances for the Hoops.
Rangers physio Paul Hunter told the club's official website: "It's a great shame. Martin has been fantastic since he joined us and it's a real blow. We wish him all the best with his recovery."