Ladhams rolled his right ankle in an awkward landing from a centre bounce ruck contest during the Swans' three-point win over North Melbourne on Saturday.
Play was held up for several minutes before Ladhams, who had only just returned from an arm injury, was driven off the field.
The former Port Adelaide ruckman will have scans to determine the full extent of the damage and the Swans are expecting bad news.
"It looks like he's got a significant ankle injury," Sydney coach John Longmire said post-match.
"I don't know how long that means but it's pretty swollen and looks pretty bad at the moment.
"We'll need (Lachlan) McAndrew and we'll just have to work through that personnel-wise.
"We still haven't had a scan, so we'll have to wait and see, but the initial diagnosis was severe ankle injury.
"That's bad ligament damage at the bare minimum."
Ladhams joins fellow talls Joel Amartey (hamstring), Paddy McCartin (concussion), Tom McCartin (concussion), Logan McDonald (ankle), Dane Rampe (neck) and Sam Reid (hamstring) on a long injury list.
Swans co-captain Callum Mills (calf) is also sidelined and none of those players are expected back until the second half of the season.
"It's not ideal. Just our talls, it's been going on all year, but it is what it is," Longmire said.
"We can't do anything about it and we've got to keep plugging forward and pushing forward and finding ways to do it."
Sydney's narrow win over North Melbourne snapped a four-match losing streak, giving them a 4-6 record ahead of a meeting with Carlton on Friday night.
The much-needed victory came when a Kangaroos interchange infringement resulted in a free kick and 50 metre penalty to Hayden McLean.
It gifted the Swans the match-winning goal in the final minute of play.
"It's great for the players," Longmire said.
"No matter how it happens, to be able to get over the line and feel good about themselves is a good thing."
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