The hard-nosed midfielder was a late withdrawal from North's round three win over Port Adelaide last Sunday, and has failed to come up from a shoulder injury in time to face the Swans.
North coach Brad Scott confirmed on Thursday afternoon that Ziebell would miss at least one more match due to the injury, suffered in North's bruising round two win over the Western Bulldogs.
Preview: Sydney Swans v North Melbourne
"He just said 'I think I'm going to be right to play', but we're not confident that if he cops another really heavy knock he won't reinjure it," Scott said.
"Against a very good contested ball side in Sydney, we know the way Jack plays, we're not really prepared to take a risk with him so we won't name him.
"But the good news is he should be right for the week after."
In better news for North fans, captain Andrew Swallow ran at full pace on Thursday and is close to returning from an Achilles injury.
"He's done a lot of training, but he's going to play at VFL level, regardless of what the temptation is for the match committee to bring him back in," Scott said.
"Hopefully he's only a week or two away from that."
Twitter: @TravKing_AFL
"He just said 'I think I'm going to be right to play', but we're not confident that if he cops another really heavy knock he won't reinjure it," Scott said.
"Against a very good contested ball side in Sydney, we know the way Jack plays, we're not really prepared to take a risk with him so we won't name him.
"But the good news is he should be right for the week after."
In better news for North fans, captain Andrew Swallow ran at full pace on Thursday and is close to returning from an Achilles injury.
"He's done a lot of training, but he's going to play at VFL level, regardless of what the temptation is for the match committee to bring him back in," Scott said.
"Hopefully he's only a week or two away from that."
Twitter: @TravKing_AFL
