Little was carried off on a stretcher wearing a neck brace after lengthy treatment following a clash of heads with Dunfermline full-back Alex Whittle in the first half of Rangers' 3-1 League One victory on Wednesday night.
The 24-year-old went straight to hospital and Rangers say it will be 2014 before he is expected to make a comeback.
Little was originally scheduled to have an operation on Thursday but he has been forced to wait.
Little wrote on his Twitter page: "Out of hospital. Unfortunately need to wait until Monday for surgery because of too much swelling! Taken back by all the msgs. Thank you."
The versatile Little has scored six goals this season after netting 25 last term.
Rangers are yet to discover the extent of the injury suffered by Richard Foster, who left Ibrox on crutches after suffering an ankle injury.
The club website said: "He has hurt his ankle but there is a lot of swelling around it and the club's medical staff will have to wait until that subsides before they can determine the specific nature of his injury."
Skipper Lee McCulloch also suffered a head wound but played on after getting six stitches and scored the opening goal from the spot in the 70th minute.
The penalty incident saw Dunfermline defender Jordan Moore sent off following a second booking for a foul on McCulloch and referee Gary Hilland booked a further eight players, three of them from Rangers.