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.

Willie Boy O'Neill, three, and Tojo O'Neill, two, formerly of Caldon Road, were last seen on 3 August.
They are believed to be in the company of their parents, Claire Watson, 32 and 39-year-old Robert O'Neill (39).
The children were reported missing after council officials became concerned for their welfare after failing to contact the family.
Willie Boy is described as being of slim build with fair hair, whilst Tojo is stocky with fair hair.
Since being reported missing to police last week, officers have made extensive inquiries in England - where there are family connections - to trace the family.
So far, there have been no positive sightings of the children, except for the whole family being seen together within the Rivergate Shopping Centre in Irvine at 14:45 on Sunday 3 August.
Police have appealed for anyone with information about the children's whereabouts to contact them urgently.

Fox was unseated after his mount, Luxford, veered sharply to the right.
Television replays showed the filly had been distracted by a stray golf ball on the course, which appeared to be thrown up by eventual winner Big Lachie.
The ball ricocheted off the helmet of another rider and across the sightline of Fox's mount.
Sandown Park in Surrey has three nine-hole golf courses close to the racetrack, but clerk of the course Andrew Cooper said they were not open on racedays.
"I am satisfied that we take all reasonable precautions to make sure that the course is as clear as we can make it but we accept that there will be some balls buried in the grass," said Cooper.
"We have a 14-strong team that walk the course, and other parts of the track, looking for golf balls.
"Even where there is netting next to the driving range we have found them. It is not a unique occurrence and we probably have this happen once every three or four years."
The afternoon ended on a more positive note for Fox as he partnered First Experience to victory.
Subscribe to the BBC Sport newsletter to get our pick of news, features and video sent to your inbox.

The former England international, who switched his allegiance to The Elephants ahead of their Nations Cup defence, came off the bench in Abu Dhabi to provide the perfect cross for Giovanni Sio who headed home a winner.
An own-goal from Wilfried Kanon had put Sweden ahead, with Yao Serge Nguessan equalising on the stroke of half-time.
24-year-old Zaha was born in Ivory Coast but has two England caps having played against Sweden in November 2012 and Scotland the following year.
As both were friendly matches, he was permitted to commit his international future to his country of birth.
The Ivorians have been preparing for the Nations Cup in the United Arab Emirates.
They will be heading to Gabon on Thursday and will play their opening Group C game on 16 January against Togo.
In other friendly internationals this weekend, Algeria were 3-1 winners over Mauritania; Burkina Faso beat Mali 2-1; Uganda defeated Slovakia 3-1; Senegal were 2-1 winners over Libya and Egypt recorded a rare victory over North African rivals Tunisia, winning 1-0.
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.
[NEXT_CONCEPT]
Police are attempting to trace two children who have been missing from the Irvine area of North Ayrshire.
[NEXT_CONCEPT]
Jockey Kieren Fox escaped unhurt when he fell from his horse in a bizarre incident involving a golf ball during a race at Sandown.
[NEXT_CONCEPT]
Crystal Palace winger Wilfried Zaha provided the decisive cross on his Ivory Coast debut as the African champions beat Sweden 2-1 in an Africa Cup of Nations warm-up match on Sunday.