The 23-year-old, who scored a try in the win, had surgery on Saturday.
"It's not great for him," director of rugby Richard Cockerill said.
He is the second Tigers pivot to fracture his jaw this season, Freddie Burns having suffered a similar injury in October.
Flanker Brendan O'Connor also faces up to six weeks out with a hamstring tear suffered in the win at Welford Road.
Williams' injury is a blow to any hopes he has of a Wales call-up for the 2016 Six Nations.
Leicester Tigers fly-half Owen Williams has been ruled out for at least eight weeks after suffering a double fracture of his jaw in Saturday's victory over Northampton Saints.