It comes as new recruit Adam Elliott prepares to join Souths' bench and face former side Newcastle for his first game in nearly a year.
Smith had been in excellent form since returning from his pre-season calf injury in round six, but re-injured himself in last week's hoodoo-busting defeat of Melbourne.
The Rabbitohs had been hopeful the issue was not serious, with Wayne Bennett naming the 2020 premiership winner in his extended squad for Sunday's away trip.
But Smith took no part in Saturday's captain's run and is now set for another stint on the sidelines, after knee injuries restricted him to only five games last season.
"He's pretty disappointed, to be honest with you, he's out for another month," Bennett said.
"He loves to play and he brings a lot to the team. But we all have our disappointments so he's got to handle it."
Elliott trained with the team on Saturday and is set to be promoted from Bennett's extended squad to the bench for his first game since last May.
A biceps injury curtailed Elliott's final season with the Knights before calf problems delayed his start to life at Souths, who offered him a one-year deal over the summer.
"He kept ringing me ... He wanted to be here, so I'm happy for him to be. He's been very good," Bennett said.
"Adam hasn't played for the latter period of last year and we're seven or eight weeks into the season and he's getting his first game.
"I admire them (players) for how they persevere and want to be back and playing with their teammates."
Kalyn Ponga, Bradman Best, Dylan Lucas, Greg Marzhew and Tyson Frizell all return from injury to give Newcastle reinforcements of their own.
Talismanic co-captain Ponga is back from a hamstring issue for his first game since round two and will resume his push to reclaim Queensland's fullback jersey.
"He's a handful, he's a very good player," Bennett said.
"Nobody's ever owned the game, you always find a way to minimise their opportunities, but at the end of the day, he'll make some that most players can't make.
"You've just got to try and keep those to a minimum. If you can do that, you'll probably manage the rest of the team."
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