The 24-year-old sustained the injury during the warm-up ahead of last Saturday's victory over Worcester Warriors and could now be sidelined for up to three months.
Williams was being considered at openside for the autumn series, but is the latest in a growing list of players to pull out of Eddie Jones's squad through injury.
"Mike felt he had done something but thought it was just a bang. But the medical guys looked at it and Mike was pulled out before the kick off," Leicester director of rugby Richard Cockerill is quoted as saying by the Leicester Mercury.
"He is in a cast and will take some specialist advice. But it looks like 8-12 weeks out – not 4-6 because of the history of the injury.
"Mike is bitterly disappointed. You would have thought that had he continued the way he has been doing for the last couple of weeks he would have had a chance to play for England."
Williams has now suffered similar injuries to his arm three times in the last 12 months.