Ted Clohesy has been called into the Cats' line-up for Saturday night's contest at Marvel Stadium and will start as the substitute.
Smith's latest setback comes a week after his scintillating Geelong debut, when he tore Fremantle apart in a 78-point win.
It remains to be seen whether the 24-year-old will be fit to return in the blockbuster clash with Brisbane at the Gabba in round three.
"He was really close (to playing against St Kilda)," Geelong coach Chris Scott said on Fox Footy before the opening bounce.
"As is our normal practice, we like to give them as long as possible.
"There was a good chance that he was going to play, and we wanted to give him right up until game time really.
"It became clear in the last 24 hours that it was the most prudent thing to wait a little bit, but that gives us an indication that he'll be right next week."
Smith missed the entire 2024 season with the Western Bulldogs because of a torn anterior cruciate ligament, before being granted his wish of a trade to Geelong.
The high-profile midfielder shone in pre-season and dominated against the Dockers with 32 disposals and one goal.
St Kilda have made four changes to their side to face the Cats, with Mitch Owens, Liam Stocker and Hunter Clark all back in, alongside debutant Isaac Keeler.
Zaine Cordy, Arie Schoenmaker, Harry Boyd and Angus Hastie were omitted after a 63-point thrashing from Adelaide in round one.
St Kilda have won their past three clashes with Geelong at Marvel Stadium.
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