Gardiner suffered the hand injury after while attempting to make a tackle in their round-six loss to former club Geelong.
Sydney coach Scott Gowans said he was unsure of Gardiner's rehabilitation timeline, admitting he is not expecting a quick return.
The Swans are already without All-Australians Chloe Molloy (knee) and Ally Morphett (foot) for the remainder of the season, while former No.1 pick Montana Ham is managing foot soreness.
"Laura will be out for extended time. We won't know how long until we get the results but it's not looking good," Gowans said on Wednesday.
"Her hand hit the body of the opposition player awkwardly. Unfortunately she's done some damage to her hand so she's off to see a specialist.
"It'll be a bonus if we see her again this season."
Ham will be a test for their upcoming clash against an undefeated North Melbourne side.
With four matches left of the home-and-away season, Sydney's prospects of making the top eight are slim.
They sit 12th on the ladder with two wins and five losses.
Elsewhere, Western Bulldogs defender Lauren Ahrens and Carlton ruck Maddy Henry have both been ruled out of the campaign with foot injuries.
Scans have confirmed that Lauren Ahrens will miss the rest of the season with a foot injury. — AFL Women's (@aflwomens) pic.twitter.com/JCVBU6GOPKOctober 8, 2024
Scans confirmed Ahrens sustained a stress reaction injury following their loss to the Kangaroos, while Henry fractured her left foot against the Brisbane Lions.
In good news for Adelaide, midfielder Abbie Ballard has avoided an anterior cruciate ligament tear to her right knee.
Ballard hurt her knee in a tackle in the second quarter of their win over St Kilda and did not return to the field after halftime.
She will miss at least one week.
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