The 31-year-old suffered the fresh setback during last weekend’s 1-0 defeat to Derby County.
Maxwell required medical treatment on the field but opted to play on as three substitutes had already been made.
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It was the goalkeeper’s second appearance since returning from a torn quadricep, an injury that kept him out for two months.
“The news is indifferent,” Critchley said.
“Maxi has got a recurrence of the quad injury he had, but hopefully it’s not as severe as what he had before.
“He certainly won’t be fit for this weekend's game against Peterborough.”
When asked if Maxwell is likely to remain sidelined throughout the Christmas and New Year programme, Critchley replied: “I would have thought so.
“As I say, it’s a recurrence of the injury he had which is obviously disappointing.
“We thought we had given him the proper rehab for as long as he required, so for it to happen again is really unfortunate because he’s a really important player for us.
“It’s certainly not like a one week injury, but I also wouldn’t want to put a timeframe on it because we’re hopeful it won’t take as long as it did last time.”
Pool’s head coach also provided an update on Reece James, who was substituted at half-time at Pride Park last week with a hamstring injury, Oliver Casey (ankle), Luke Garbutt (knee), Kevin Stewart (ankle), Matty Virtue (ACL), Grant Ward (achilles) and Gary Madine (groin).
“We got better news with Reece James,” Critchley said.
“He’s not torn his hamstring or anything, so we’re still hopeful he could be involved this weekend.
“Gary Madine has trained this week, Luke Garbutt has been training, Kevin Stewart not quite yet. Oliver Casey has been training for the last couple of weeks, so he’s fine.
“Matty Virtue has been on the grass doing some running and a bit of ballwork for a number of weeks now, but slow and steady will win the race for him.
“Wardy is a bit behind that. He’s just come out of his boot recently and is beginning to put a bit more weight on it, so he will start to step that up in the next few weeks.
“They’re both positive and I am thinking about them, but not from a playing point of view at this moment in time.”
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