Smith saw a specialist last week about a problem stemming from the ankle fracture he suffered away at Oxford in March and the left-back missed the Spireites' 1-0 home victory over Accrington on Saturday.
Exploratory surgery revealed no serious damage and the 26-year-old, last season's player of the year, will not need a second operation.
It is not yet known how long Smith will be out, although it is likely he will miss out again when AFC Wimbledon visit the Proact Stadium at the weekend.
"No major surgery was required, which is good news," Chesterfield physio Jamie Hewitt told the club's official website.
"They found a bit of scar tissue in the ankle joint so he's had it all cleaned out. He's out of hospital now and on crutches."
"We'll assess him at the end of the week and have a better idea of timescale then."
Ritchie Humphreys filled in on the left side of defence in Smith's absence against Accrington as the Spireites maintained their two-point lead at the top of Sky Bet League Two.
Meanwhile, the club's only other absentee, centre-half Matty Brown, is continuing his rehabilitation from a hamstring injury.