Smith suffered the injury during the first half of the Spireites' away win at Oxford last weekend and missed the defeat at Torquay on Tuesday night while the club's medical staff ascertained the extent of the problem.
Scans have shown that the left-back has broken a bone at the top of his foot.
Blues boss Paul Cook confirmed: "There's damage to the bone and with so few matches remaining that means he won't play again (this season), which is a big blow."
Meanwhile, midfielder Craig Clay has resumed training following a hernia operation last month.
"He has joined in today (Thursday), and when I say joined in I mean as a first step towards a return to full fitness," said Cook. "He won't be involved at the weekend but maybe he has a chance of being included over the Bank Holiday weekend against Burton and Port Vale."
- Sports & Recreation