Skalski missed last week's game against Syracuse, but Swinney said the team had expected the injury to be minor. A subsequent MRI on Monday revealed more significant damage, and Swinney said the senior will need surgery.
"That's a pretty big loss for us," Swinney said. "He's going to miss a few games, unfortunately. We'll have to see how it all goes and how quickly responds, but he's a great football player. ... He's truly the heart and soul of our defense."
Skalski is one of a number of Clemson starters to miss time this year. Defensive end Justin Foster has been out all year, and Xavier Thomas returned two weeks ago but has been slowly reintroduced to action.
Swinney said cornerback Derion Kendrick (knee), who was out against Syracuse, was "sore" but is likely to return this week.
"He's progressing really well," Swinney said.
At linebacker, Skalski's role will fall to sophomore Jake Venables, son of Clemson defensive coordinator Brent Venables.
The younger Venables had four tackles in a starting role against Syracuse last week, and he has racked up 3.5 tackles for loss on the season.
"He did a great job last week and really played well for us," Swinney said. "This is a game, especially, that they're a challenge formational and schematically in what they do. A lot of formations and shifts that you have to be able to process, and I'm really thankful we have a veteran guy like Jake."
Swinney also said outside linebacker Mike Jones was "day to day" with soreness, but he did not say whether Jones would miss action this week.