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Kranjcar will definitely miss Sunday's Scottish League Cup semi-final against Glasgow rivals Celtic.
Ibrox medics are now waiting for the swelling to go down before they are able to fully assess the problem.
The summer signing from New York Cosmos has made 15 appearances for Mark Warburton's side.
Kranjcar struggled for match fitness when he first arrived in Scotland but has been more influential in recent weeks.
The injury further depletes the Scottish Premiership outfit's midfield options, with Kranjcar's former Queens Park Rangers team-mate, Joey Barton, serving a club suspension.
Barton, who signed after leaving Burnley this summer, appears unlikely to play for Warburton's side again after a fall-out with the manager.
Kranjcar, who played 81 times for Croatia, joined New York Cosmos earlier this year after leaving Dynamo Kiev.
He previously played for Dinamo Zagreb, Hajduk Split, Portsmouth and Tottenham Hotspur.
Rangers midfielder Niko Kranjcar has suffered a knee injury in training that could sideline the 32-year-old Croat for months.