He joins James Haskell (foot), Jack Clifford (ankle) and Sam Jones (broken leg) on the sidelines, the latter having been injured in a judo session at an England training camp.
"It's bitterly disappointing with England on the horizon," Leicester director of rugby Richard Cockerill said on Tuesday of Williams' latest misfortune.
"Unfortunately he's re-fractured his arm that he broke last year. It will heal in 8-12 weeks," he told the BBC.
"It's the same arm and fracture site. Historically, these things are notoriously difficult to clear up. They have a history of coming back.
"We have done all the right things and he has done everything he can do but it is purely bad luck."
The forward broke a bone in his forearm last December and his season ended when he broke it again in January.
(Writing by Ken Ferris; Editing by Greg Stutchbury)
