The 22-year-old needs an operation on a hip injury he sustained in a friendly against Burnley last Tuesday.
Shrimps manager Jim Bentley also revealed they had turned down a six-figure sum for last season's top scorer, who scored 16 times in all competitions.
"It is a massive loss for us and a huge blow for Jack as well," Bentley told the club's official website.
"He is absolutely devastated and can't believe that he is going to be out for so long. He needs an operation and will be on crutches for some time and I don't think we will see him until some time in 2014.
"But we have to maintain our belief and, as I often say, where one door closes another one opens and it gives others a chance to show what they can do and make their mark.
"The lads have been brilliant so far and I am sure that with the togetherness we have we can put this to the back of our minds and look forward to seeing Jack back in action in the second half of the season."
Redshaw's injury means he is unlikely to be leaving the Globe Arena any time soon and Bentley was pleased with his board's resolve in rejecting such a large fee.
He added: "The bid was a large one for Jack but I am delighted that the board backed me and turned it down.
"It shows that despite the financial climate they were prepared to keep a player who was an important part of our plans and integral to what we are trying to build here."
- Sports & Recreation
- Jim Bentley