The loss of Williams, who was the club’s player of the season in 2024-25, is a huge blow for Cardiff after their encouraging start to this campaign.
Josh McNally, George Nott, Ben Donnell and Rory Thornton are second-row options along with academy prospect Tom Cottle.
The Blue and Blacks finish the first block of the URC with a trip to Dragons and home fixture against Edinburgh before a break for the autumn internationals.
Williams won his eighth cap in July’s win against Japan and would have been a leading contender to be in Steve Tandy’s first squad for the autumn Tests against Argentina, the Brave Blossoms, New Zealand and South Africa.
Wales used Dafydd Jenkins, Will Rowlands, Freddie Thomas, Ben Carter, James Ratti and Williams in the second row last season.