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.
Manager Paul Cook has a handful of other players, who he did not name, nursing knocks and he will assess their fitness nearer the game.
"There's a lot of ifs and buts and bumps and bruises and we'll probably have to wait until after training on Friday to see what we've got," said Cook.
Armand Gnanduillet's knocks are not clearing up and the young striker will remain on the sidelines.
However, Craig Clay has resumed training following a hernia operation last month but this game will come too soon for the midfielder.