The dual All Australian was tackled by Will Graham at People First Stadium on Friday night and his ankle twisted awkwardly under him.
Gulden was in agony as trainers helped him from the ground, amid speculation it could be a syndesmosis injury.
"It is disappointing ... he's off getting some scans at the local hospital ... we won't get those results back for another 24 hours. He's in a bit of pain," Swans football boss Leon Cameron told Fox Footy at half-time.
Gold Coast key position player Mac Andrew did not last the opening minute of the game, forced off with a chest injury after a collision in the first marking contest.
Suns teammates Charlie Ballard (ankle), David Swallow (knee) and Lachie Weller (hamstring) were also taken out of the game after they were hurt.
Gold Coast kicked the first three goals of the last quarter and pulled to within four points, but the Swans kicked clear with their own three-goal run to win 12.12 (84) to 8.15 (63).
Already on Friday, Port Adelaide confirmed Zak Butters is out for at least six weeks after knee surgery and Western Bulldogs captain Marcus Bontempelli will have a similar spell because of his calf muscle injury.
Despite fielding an undermanned team, Sydney kicked the first four goals of the game and were never headed.
Former key defender Tom McCartin impressed in his new role as a forward, kicking four goals.
New Suns captain Noah Anderson racked up a game-high 35 disposals, with nine clearances.
The Suns had plenty of chances, but were wasteful in attack and losing Andrew at the start of the game clearly hampered their forward structure.
They did not kick a goal from late in the second term until early in the last.
Swans captain Callum Mills (foot) will miss their opening round home match next Friday against Hawthorn, while ruckman Brodie Grundy is in doubt with a knee injury.
Several Sydney stars were rested for the Gold Coast game, including Isaac Heeney, Chad Warner and Dane Rampe.
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