Smith, 26, went off with a foot injury 28 minutes into the Spireites' 1-0 win at Oxford on Saturday.
The club's medical staff are still assessing the extent of the problem but the player may already be a doubt for Saturday's home game against Plymouth, which sees the return of former manager John Sheridan.
Conor Townsend will replace Smith at left-back at Plainmoor on Tuesday, freeing up a space in midfield.
The fit-again Drew Talbot, Danny Whitaker, Mark Randall or on-loan Manchester City winger Alex Henshall will come into the team.
Jack Lester is also an option for boss Paul Cook, although the veteran striker is usually saved for home matches these days and is likely to be on the bench with the visit of Plymouth just four days after the Gulls game.
Following three starts in eight days at the start of the month, young striker Armand Gnanduillet was absent at Oxford at the weekend with what Cook described as "a few knocks".
Cook thinks it will be a couple of weeks before the Frenchman is ready to play again.
- Sports & Recreation