Smith, 20, only joined League Two Alex on loan earlier in July until January 2017 and was hurt in a friendly against Bolton Wanderers on Friday.
"The good thing is he hasn't got any ligament damage or fracture," boss Steve Davis told BBC Radio Stoke.
"He's got bruising to the bone and it's difficult to know how long it'll take."
Davis, though, is hopeful Smith will be back in a matter of weeks.
"They've said do nothing for 10 days and reassess to see if he can put any load on it so he'll go back to Newcastle for a short spell while he can't do anything," Davis, 51, said.
"You could be looking at three weeks or it could be more or less than that.
"The good thing about him going back is that they have got things there medically that we haven't got here and can get the bruising down quicker."
With finances tight at Gresty Road, the loss of Smith - one of only three new signings this summer - has left Davis with a potential hole to fill.
"If there is someone out there who fits the bill I can put it to the board," Davis said. "We're close to the budget and we're still looking at three or four players to renew contracts.
"But there's a hole there and we're going to be light in that position - we need to do something now rather than leave it until January."
Midfielder Liam Smith is to return to parent club Newcastle United to recover from an ankle injury suffered during pre-season with Crewe Alexandra.