The 24-year-old - signed on a permanent ?15million deal from Liverpool after a loan spell last season - had looked to be on his way back to full fitness following an Achilles problem.
However, he then broke down during a training session earlier this week with a foot injury when he aggravated the plantar fascia tissue which supports the arch, and is so now set for another extended spell on the sidelines.
Press Association Sport understands Carroll has travelled to Europe - boarding a plane for Belgium on Friday morning - to begin a rehabilitation programme which the club hopes will not require an operation, but equally no time frame has been set for a possible return to full match fitness.
While Allardyce is confident the 6ft 3ins former Newcastle frontman will recover from the setback, the Irons boss understands there are personal battles for him to overcome ahead of a season which, if all goes well, could end with playing for England at the 2014 World Cup in Brazil.
"It is a big challenge for Andy because he has got to be mentally really tough now," said Allardyce.
"He has to be really, really focused and we have got to make sure we keep his spirits up whenever we get the chance because it is a lonely place to be when you are injured, and certainly for the length of time he has been injured.
"This will make him feel pretty low for a while, but he has to battle through that and we will look after the psychological side as well as the physical side. At the end of the day it is just about getting him fit as quick as we possibly can."
Allardyce revealed the nature of Carroll's latest fitness problem was linked to the centre-forward's style of play.
"What you find on my research is that this is an unusual injury for footballers. It probably more revolves around people like ballerinas and basketball players because of the bounding side of it," the West Ham manager said.