The 28-year-old sustained the injury in an accidental collision last week and after a consultation with a specialist in Manchester over the weekend he has been ordered to rest.
Kirkland has been troubled by a back problem for several months now but this new injury is a blow to him and the team.
Crocked: Kirkland has been told he has to rest
This is a completely new injury, I must stress that, it could have happened to anyone,' said manager Roberto Martinez.
'I'm disappointed to lose him but the diagnosis is much better than it could have been and Chris should be back in full training within a fortnight hopefully.
'It's important that we get him back in contention as soon as possible, but we have to be certain the injury is healed before risking him.'
CLICK HERE FOR ALL THE MIDWEEK TEAM NEWS IN THE BARCLAYS PREMIER LEAGUERichard Evans, Wigan's head of sports science, said fortunately there was no break, which meant Kirkland's lay-off would not be too long.
'The consultant was happy with the alignment of the bone, there is certainly no fracture,' he said. 'He has assured us it will heal completely given a rest period. It could have been a lot worse.'
In Kirkland's absence Serbia international Vladimir Stojkovic, signed on loan from Sporting Lisbon earlier this month, is likely to deputise having made his debut in the 2-2 FA Cup fourth-round draw at Notts County at the weekend.
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